A rhombus has side of length 60 units each and the lengths of its perpendicular diagonals are in the ratio of 2 to 1. What is the area of the rhombus, in square units?

Answers

Answer 1

Answer:

2880 square units

Step-by-step explanation:

Since the area of a rhombus, A = d₁ × d₂/2 where d₁ and d₂ are its diagonals. Given that d₁:d₂ = 2:1, d₁/d₂ = 2/1, so d₁ = 2d₂. Also, the length of side of the rhombus L = 60 units.

We find the length of the diagonal by Pythagoras' theorem since the diagonals are perpendicular to each other and bisect each other at their mid point.

The mid point of d₁ = d₁/2 and the midpoint of d₂ = d₂/2.

By Pythagoras' theorem,

L² = (d₁/2)² + (d₂/2)²

L² = d₁²/4 + d₂²/4

Now, d₁ = 2d₂

So, L² = (2d₂)²/4 + d₂²/4

L² = 4d₂²/4 + d₂²/4

L² = d₂² + d₂²/4

L² = 5d₂²/4

d₂² = 4L²/5

taking square root of both sides,

√d₂² = √(4L²/5)

d₂ = 2L/√5

Since L = 60 units, then

d₂ = 2L/√5

d₂ = 2(60)/√5

d₂ = 120/√5

rationalizing the denominator by multiplying the numerator and denominator by √5, we have

d₂ = 120/√5 × √5/√5

d₂ = 120√5/5

d₂ = 24√5 units

So, our area A = d₁ × d₂/2

Since d₁ = 2d₂, our area is

A = 2d₂ × d₂/2

A = d₂ × d₂

A = d₂²

substituting d₂ = 24√5, we have

A = d₂²

A = (24√5)²

A = (24)²(√5)²

A = 576 × 5

A = 2880 square units


Related Questions

Help me please with this question

Answers

Answer:

107cm

Step-by-step explanation:

The the answer is 107 because you have to add up all of the numbers.

I really need help on this one I

Answers

Answer:

60

Step-by-step explanation:

60

What is the value of x in the circle on the right?​

Answers

X=sqrt of 29

Use Pythagorean Theorem!

a^2+b^2=c^2

C is the hypotenuse, so the biggest side, for us it’s 10.

9^2+x^2=10^2

81+x^2= 100

x^2= 29

X= sqrt29

Since x is the radius on both sides, the value will be the same :)

The area of a rhombus is 36 sq. cm. If its perimeter is 16cm, find its altitude.​

Answers

HELP MEEE I NEED HELP TOO

Answer:

Perimeter of rhombus =4×l

16=4l

l=16/4=4

its length =4cm

area of rhombus=36cm²

base× height (here base=length)=36cm²

4h=36

h=36/4=9

:.altitude of rhombus is 9cm.

LAST QUESTION PLS HELP. (It's not solve for x)

Answers

Answer:

40

Step-by-step explanation:

So, if the angle shown, one of them is 70. the other is 110, because line is 180 degress, 180-70 = 110. C is 110. But, we need to find B. 13x + 6 must also be 70 degrees. 70-6 = 64. 64/13 = about 5. A is 100. The inner angles are 70+70+N. Angles in triangle are 180, so N is 180-70-70, which is 180-140. The B is 40 degrees.

Answer:

m∠ABC = 26°

Step-by-step explanation:

13x+6 + 8+3x + 70 = 180

16x + 84 = 180

16x = 96

x = 6

m∠B = 8+3(6) = 26°

Each member of the swim team must pay $76 to join the team. There are 376 members. How much does the team receive in dues?

Answers

Answer:

$28,576

Step-by-step explanation:

$76 (amount that each member pays) * 376 (total members) = $28,576 (amount that will be received in dues)

I hope this helps :)

Find the missing fraction. What is the ??? equal to? (the fractions aren't in order)

1/12, 1/27, 1/6, 1/9, ???, 1/3

if you could help that would be amazing! thanks!

Answers

Step-by-step explanation:

1/6 divided by 3=1/2.

I think this is the answer

Please please help i need thisrigt now

Answers

Answer:

oh i can't see the picture!!!

Step-by-step explanation:

what is 1.5 as a fully simplified fraction , thank youuuuu !!

Answers

Explanation: 1.5 is the same thing as "one and five-tenths," or "one and five over ten, or one and half," which is written as 112 as a fraction.

hallar el área de un triangulo rectángulo isósceles cuyos lados miden 10cm cada uno
helpppp

Answers

34.1 because that is the correct answer

PLEASE HELP ASAP !!!!!

Answers

Answer:

The correct answer is

b) DEF=QRS

HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
HELP I NEED HELP ASAP

Answers

Answer: C

Step-by-step explanation:

Answer:

the answer is 8 I think lol

A placement test is administered to collegiate freshmen. The test is known to be approximately normal with a mean of 65 and a standard deviation of 5. Sheila scored a 59 on this test. Does this score place Sheila in the bottom 10% of test takers?

Answers

Answer: D. She is above 11.5% of test takers

Step-by-step explanation:

So logically we can eliminate like 3 answers and let me explain why

So first we can eliminate both A and B because the question asks "Does this score place Sheila in the bottom 10% of test takers?" If the answer were yes she wouldn't be "above 8.5%" or "above 11.5%" because she would be below.

So that would leave both C and D right. Lets look at C first. It says "No, she is above 8.5% of test takers" But if she is above 8.5% she could hypothetically be in the 9% or the 9.5% of test takers. Since this answer doesn't gurantee she would be above 10% we can't choose it. Now D it says "No, she is above 11.5% of test takers" This is correct because She is not in the bottom 10% because according to the empirical rule she is I would say around or just under 16% of test takers. Also the 11.5% part gurantees that anything above the number 11.5 is greater than 10%. Unlike in C which only says the number is greater than 8.5 which means the number could be 8.6 which is NOT greater than 10.

Which line is tangent?

Answers

TR

Best luck with your studying
TSR is a tanget line

Heather has divided $5600 between two investments, one paying 9% the other paying 5%. If the return investment is $396, how much does she have in each investment?

Answers

Answer:

x = 2700 y=2900

Step-by-step explanation:

x+y = 5600

5/100 x + 9/100 y = 396

x+y=5600

5x+9y=39600

5x+5y = 28000

5x+9y=39600

-4y = -11600

y= 2900

x = 5600-2900 = 2700

0.9x. +0.6(5600-x)=396
9x + 6 (5600-x) =39600
9x + 33,600 - 6 = 39600
3x = 6000
X = $2000




So 2000 invested at 9% and 3000 invested at 5%


09(2000) + .05(3000) = 3300

please help!!!!!! :)

Answers

Answer:

Step-by-step explanation:

2w+11=109

2w=98

w=49°

Find the value of the expression below for x=3
x^2+5

Answers

Answer: 14

Step-by-step explanation: 3 to the second is 3 twice EX. 3x3=9, 9+5=14

Answer: x= −5 /2 + 1 /2 √37 or x= −5 /2 + −1 /2 √37

Step-by-step explanation:

Step 1: Subtract 3 from both sides.

x2+5x−3=3−3

x2+5x−3=0

For this equation: a=1, b=5, c=-3

1x2+5x+−3=0

Step 2: Use quadratic formula with a=1, b=5, c=-3.

x= −b±√b2−4ac /2a

x=

−(5)±√(5)2−4(1)(−3) /2(1)

x= −5±√37 /2

x= −5 /2 + 1 /2 √37 or x= −5 /2 + −1 /2 √37

What is the image point of (2,9) after the transformation
T-1,-4 o ry=x?

Answers

Answer:8,-2

Step-by-step explanation:

Delta math

write this expression without grouping symbols.
-3x(2x+5)

Answers

Answer:

− 3 ( 2 + 5 )

Step-by-step explanation

Simplifica  

Distribuye

− 3 ( 2 + 5 ) − 6 2 − 1 5

Solución

− 6 2 − 1 5

help please... Thank you in advance ​

Answers

Answer:

156

Step-by-step explanation:

A roller coaster is at the top of a 72 m hill and weighs 134 kg. The coaster (at this moment) has____________ energy. Calculate it.
A. Kinetic Energy and 347,328J
B. Kinetic Energy and 9,648J
C. Potential Energy and 9,648J
D. Potential Energy and 94,550.4J

Answers

Answer:C

Step-by-step explenation: m=134kg,h=72m,g=10m/s

PE=mgh

PE=(134kg)(10m/s^2)(72m)

PE=964800J

A paper company needs to ship paper to a large printing business. The paper will be
shipped in small boxes and large boxes. The volume of each small box is 6 cubic feet
and the volume of each large box is 22 cubic feet. A total of 22 boxes of paper were
shipped with a combined volume of 324 cubic feet. Write a system of equations that
could be used to determine the number of small boxes shipped and the number of
large boxes shipped. Define the variables that you use to write the system.

Answers

Answer:

10 small boxes and 12 large boxes

Step-by-step explanation:

Let x = number of large boxes

Let y = number of small boxes

We are told that;

volume of each small box = 6 cubic feet

volume of each large box = 22 cubic feet.

Total volume = 324 ft³

Thus;

6x + 22y = 324 - - - (eq 1)

We are told that 22 boxes of paper were shipped.

Thus; x + y = 22 - - - (eq 2)

Making x the subject in eq 2 gives;

x = 22 - y

Put 22 - y for x in eq 1;

6(22 - y) + 22y = 324

132 - 6y + 22y = 324

16y = 324 - 132

16y = 192

y = 192/16

y = 12

So, x = 22 - 12 = 10

a = 5bc
b = -4 and c = -3
Work out the value of a.

Answers

Step-by-step explanation:

a=5*-4*-3

a=-2

hope this helps

Determine the amounts horizontally and vertically that the given point was translated.


1. A translated to B
2. A translated to C
3. D translated to B
4. C translated to D
5. B translated to C

Answers

Answer:

OPTION B I THINK SOOOO

PLS MAKA ME BRAINIST PLS

Step-by-step explanation:

HOPE YOU HELP

Answer:

1. x = 1

   y = -7

2. x = 9

   y = -5

3. x = -6

  y = -5

4. x = -2

  y = 3

5. x = 8

   y = 2

Step-by-step explanation:

Count until you get from the first point to the next.

help meee plsssss

:)

Answers

-3(is less than)1 and 5(is less than or equal to) 25

I need help who ever get it right get brainly

Answers

Answer:

m<a = m<c since those two angles are vertical angles.

m<a + m<b = 90⁰ since, if you look closely m<a and m<b forms a 90⁰ angle that means it is equal to 90⁰.

Hope this helps and I would appreciate if you give me the brainlist or not thank you :) !!

What are the coordinates of the point on the directed line segment from (-10, -5) to (5, 1) that partitions the segment into a ratio of 1 to 2?

Answers

if you make a graph and add the coordinates on the graph you can use that find out how it creates a ratio of 1:2

4. Divide z(5z2 - 80) by 5z (z+4)​

Answers

Answer:

z-4

Step-by-step explanation:

z(5z²-80) ÷ 5z(z+4) = z-4

Step-by-step explanation:

Given: z(5z²-80) ÷ 5z(z+4)

Calculation:

First we factor numerator z(5z²-80)

Take out 5 from 5z²-80 and we get 5z(z²-16)

Now we factor 16 = 4²

5z(z²-4²)

Using formula, (a²- b²)=(a+b)(a-b)

5z(z²- 4²)⇒5z(z+4)(z-4)

Simplified fraction

5z(z+4)(z-4) ÷ 5z(z+4)

Cancel like factor from numerator and denominator

⇒ z-4

Thus, z(5z²-80) ÷ 5z(z+4) = z-4

m
n
hk
b
a
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V
Angle a = 126. What is the measure of angle b? Explain how you calculated your answer.
Angle a = 126 Write an equation(s) in terms of b to find the measure of angle h.
Calculate the measure of angle h, using the equation(s) you wrote for Part B.
How would knowing the measure of angle y change the equation(s) you wrote in Part B to find the measure of angle h?
2021 Muminate Education Inc

Answers

Answer:

um here

Your input: factor x2+4x+3.

To factor the quadratic function x2+4x+3, we should solve the corresponding quadratic equation x2+4x+3=0.

Indeed, if x1 and x2 are the roots of the quadratic equation ax2+bx+c=0, then ax2+bx+c=a(x−x1)(x−x2).

Solve the quadratic equation x2+4x+3=0.

The roots are x1=−1, x2=−3 (use the quadratic equation calculator to see the steps).

Therefore, x2+4x+3=1(x+1)(x+3).

(x2+4x+3)=1(x+1)(x+3)

Step-by-step explanation:

What kind of number is
5 1/4

Answers

Answer:

I think you're talking about mixed numbers

Step-by-step explanation:

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