Question

Which is a true statement about an isosceles right triangle? A.The hypotenuse is square root 3 times as long as either leg. B. The hypotenuse is square root 2 times as long as either leg. C. Each leg is square root 2 times as long as the hypotenuse. D. Each leg is square root 3 times as long as the hypotenuse.

Answer 1

An isosceles right triangle is a special right triangle where the legs are represented by x and the hypotenuse by x*the square root of 2 so your answer is B.

Answer 2

B. The hypotenuse is square root 2 times as long as either leg.

Explanation:

The answer is B.

Let's use Pythagoras to prove it.

`h^2=a^2+b^2`

In this case since its an isoceles right triangle, a and b most be the same.

Let's say that the measure of the sides that are equal is x and the hypotenuse is h.

Pythagoras tells us the following:

`h^2=x^2+x^2`

Solving for h:

`h=√(x^2+x^2) =√(2x^2)=x√(2)`

The hypotenuse is square root 2 times as long as the sides, in this case x wich could be any number.