Question

A = (2, -5); B = (0, -5); C = (2, 5)

The sum of the squares of the lengths of the legs of the triangle is ____

The square of the length of the hypotenuse of the triangle is ____​

Answer 1

The sum of the squares of the lengths of the legs of the triangle is 104

The square of the length of the hypotenuse of the triangle is 104

Explanation:

Looking at the coordinate values (or better still plotting and examining the points on a graph) we see that

AC is a vertical leg with length = 10 (5 - (-5)) , same x coordinates

AB is the base horizontal leg with side = 2 (2-0), same y-coordinates

The sum of the legs of the triangle = 10² + 2² = 100 + 4 = 104

The square of the length of the hypotenuse is also 104 since it is a right triangle

The hypotenuse = √104= 10.2