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

Answer:

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

Step-by-step 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:

$h=\sqrt{x^2+x^2} =\sqrt{2x^2}=x\sqrt{2}$

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

Answer 2

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.