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)=(1)/(2)*(base)*(height)}}}`

Now , here substitute the respective values ,

`\implies \sf (1)/(2)*(base)*(height)=128m^2`

`\sf\implies (1)/(2)* x * x = 128m^2`

`\sf \implies (x^2)/(2)=128m^2`

`\sf\implies x^2=128*2 m^2`

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

`\sf\implies x=√(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.