Triangle MRN is created when an equilateral triangle is folded in half.

Triangle N R M is shown. Angle N R M is a right angle. An altitude is drawn from point R to point S on side M N to form a right angle. The length of N S is 6, the length of S M is 2, the length of R M is x, the length of N R is y, and the length of R S is z.

What is the value of y?

2 StartRoot 3 EndRoot units
4 units
4 StartRoot 3 EndRoot units
8 units

The value of [tex]y[/tex] will be [tex]4\sqrt{3}[/tex] .

Triangle is a three sides two dimensional surface having three angles.

We have,

[tex]\triangle MRN[/tex] , [tex]\triangle RSM[/tex] and [tex]\triangle RSN[/tex],

And, [tex]NS =6,\ SM=2,\ RM=x,\ NR=y,\ RS=z[/tex]

Now,

We have right angle [tex]\triangle MRN[/tex],

Using Pythagoras theorem,

[tex]x^2+y^2=8^2[/tex]

[tex]x^2+y^2+=64\[/tex]     [tex].....(i)[/tex]

Now, We have right angle [tex]\triangle RSN[/tex],

Again Using Pythagoras theorem,

[tex]z^2+6^2=y^2[/tex]

⇒[tex]z^2=y^2-36[/tex]     [tex].....(ii)[/tex]

Now, We have right angle [tex]\triangle RSM[/tex],

Again Using Pythagoras theorem,

[tex]z^2+2^2=y^2[/tex]

⇒[tex]z^2=x^2-4[/tex]     [tex].....(iii)[/tex]

Now comparing equation [tex](ii)[/tex] and equation  [tex](iii)[/tex],

We get,

[tex]x^2-4=y^2-36[/tex]

We get,

[tex]x^2-y^2=-36+4[/tex]

[tex]x^2-y^2=-32[/tex]     [tex].....(iv)[/tex]

Now,

Adding equation [tex](i)[/tex] and equation  [tex](iv)[/tex], i.e.

[tex]x^2+y^2+=64[/tex]

[tex]x^2-y^2=-32[/tex]

We get,

[tex]2y^2=96[/tex]

[tex]y^2=48[/tex]

[tex]y=\sqrt{48}[/tex]

[tex]y=4\sqrt{3}[/tex]

So, the value of [tex]y[/tex] is [tex]4\sqrt{3}[/tex]

Hence, we can say that the value of [tex]y[/tex] will be [tex]4\sqrt{3}[/tex]  which is given in option (b).

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Answer:

its c

Step-by-step explanation:

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