Question

if the area of a right isosceles triangle is 128 sq . m, what will be length of the identical side of the triangle​

Answer 1

$\large\underline{\underline{\red{\sf \blue{\longmapsto} Step-by-step\: Explanation:-}}}$

Given that area of an isosceles triangle is 128m² .

And the triangle is right Angled ∆ .

So , the measure of sides along 90° that is perpendicular and the base will be equal .

Let us say that each of the equal sides is x .

Then , we can find the area of the triangle as ,

$\boxed{\bf{\red{ Area_{triangle}=\dfrac{1}{2}\times(base)\times(height)}}}$

Now , here substitute the respective values ,

$\implies \sf \dfrac{1}{2}\times(base)\times(height)=128m^2$

$\sf\implies \dfrac{1}{2}\times x \times x = 128m^2$

$\sf \implies \dfrac{x^2}{2}=128m^2$

$\sf\implies x^2=128\times2 m^2$

$\sf\implies x^2=256 m^2$

$\sf\implies x=\sqrt{256m^2}$

$\underline{\boxed{\red{\sf\longmapsto x=16m}}}$

Hence the value of value of identical side of the triangle is 16m .

Answer 2

Let's see. What is a right isosceles triangle?

A right isosceles triangle is a triangle with one right angle with at least two equal sides. In this case, it would have to be ONLY two because it has a right triangle.

What is the formula for the area of an isosceles triangle?

When y = the identical side lengths of the triangle,

and A = area,

(y × y) ÷ 2 = A

Note: Remember to compute from left to right! :)

We divide by two because when you multiple the two identical sides, you would get a square. However, we're trying to find the right isosceles triangle, and we divide by two.

Now, we can plug-in our values!

(y × y) ÷ 2 = 128

(y × y) = 64

Now, we square root both sides!

y = √64

y = 8

The length of the identical sides of the triangle is 8 meters.