The diagonal of a square is 8 cm.
What is the length of the side of this square?
Give your answer as an exact surd in its simplest form
Answers
the length of the side of this square is [tex]4\sqrt{2} \:or \:5.65[/tex]cm
Answer:
Solutions Given:
let diagonal of square be AC: 8 cm
let each side be a.
As diagonal bisect square.
let it forms right angled triangle ABC .
Where diagonal AC is hypotenuse and a is their opposite side and base.
By using Pythagoras law
hypotenuse ²=opposite side²+base side²
8²=a²+a²
64=2a²
a²=[tex]\frac{64}{2}[/tex]
a²=32
doing square root on both side
[tex]\sqrt{a²}=\sqrt{32}[/tex]
a=±[tex]\sqrt{2*2*2*2*2}[/tex]
a=±2*2[tex]\sqrt{2}[/tex]
Since side of square is always positive so
a=4[tex]\sqrt{2}[/tex] or 5.65 cm
Answer:
Given :
↠ The diagonal of a square is 8 cm.
To Find :
↠ The length of the side of square.
Using Formula :
Here is the formula to find the side of square if diagonal is given :
[tex]\implies{\sf{a = \sqrt{2} \dfrac{d}{2}}} [/tex]
Where :
➺ a = side of square ➺ d = diagonal of squareSolution :
Substituting the given value in the required formula :
[tex]{\dashrightarrow{\pmb{\sf{ \: a = \sqrt{2} \dfrac{d}{2}}}}}[/tex]
[tex]{\dashrightarrow{\sf{ \: a = \sqrt{2} \times \dfrac{8}{2}}}}[/tex]
[tex]{\dashrightarrow{\sf{ \: a = \sqrt{2} \times \cancel{\dfrac{8}{2}}}}}[/tex]
[tex]{\dashrightarrow{\sf{ \: a = \sqrt{2} \times 4}}}[/tex]
[tex]{\dashrightarrow{\sf{ \: a = 4\sqrt{2}}}}[/tex]
[tex]{\dashrightarrow{\sf{\underline{\underline{\red{ \: a = 5.65 \: cm}}}}}}[/tex]
Hence, the length of the side of square is 5.6 cm.
[tex]\underline{\rule{220pt}{3pt}}[/tex]
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