Question

If the altitude of an isosceles right triangle has a length of x units, what is the length of one leg of the large right triangle in terms of x?

Answer 1

We Know, isosceles triangle has two same sides & one larger side.
It would be: larger side = √x + √x = √2 x

So, your final answer is √2x

Hope this helps

Answer 2

The length of one leg of the larger right triangle be
`√(2)x` unit.

Explanation:

If the altitude of an isosceles right triangle has a length of x units.

The legs of right angle triangle are x units.

In right angle triangle altitude is one side of triangle.

Base (B) = x and Perpendicular (P) = x

Let hypotenuse (H) be y units

Using pythagoureous theorem

`H^2=P^2+B^2`

`y^2=x^2+x^2`

`y^2=2x^2`

`y=√(2)x`

Hence, The length of one leg of the larger right triangle be
`√(2)x` unit.