Question

In a 45°-45°-90° right triangle, what is the length of each leg if the hypotenuse has a length of 68√2?

In a 45°-45°-90° right triangle, what is the length of each leg if the hypotenuse has a length of 68√2?

Answer 1

In a 45°-45°-90° right triangle, the lengths of the legs are equal, and the relationship between the legs and the hypotenuse is given by:

\[
\text{Hypotenuse} = \text{Leg} \times \sqrt{2}
\]

Given that the hypotenuse is \( 68\sqrt{2} \), we can set up the equation:

\[
68\sqrt{2} = \text{Leg} \times \sqrt{2}
\]

To find the length of each leg, we divide both sides of the equation by \(\sqrt{2}\):

\[
\text{Leg} = \frac{68\sqrt{2}}{\sqrt{2}} = 68
\]

Therefore, the length of each leg in the triangle is:

\[
\boxed{68}
\]