Question

1. one leg of an isosceles right triangle has length 50 feet.

a. write an equation that you could use to find the length of the triangles hypotenuse.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs, and \(c\) is the hypotenuse.

Step2: Identify legs in isosceles right triangle

In an isosceles right triangle, the two legs are equal. Given one leg \(a = 50\) feet, so the other leg \(b=50\) feet. Let \(c\) be the hypotenuse.

Step3: Substitute values into theorem

Substitute \(a = 50\) and \(b = 50\) into \(a^{2}+b^{2}=c^{2}\), we get \(50^{2}+50^{2}=c^{2}\).

Answer:

The equation is \(50^{2}+50^{2}=c^{2}\) (where \(c\) represents the length of the hypotenuse).