Question

2)

Apply the Pythagorean Theorem to determine the correct statements.

A) If the sides of a right triangle are of length 8 and 15, its hypotenuse is 17.
B) If the sides of a right triangle are of length 7 and 24, its hypotenuse is 35.
C) If the sides of a right triangle are of length 9 and 40, its hypotenuse is 41.
D) If the sides of a right triangle are of length 21 and 28, its hypotenuse is 36.
E) If the sides of a right triangle are of length 12 and 16, its hypotenuse is 20.

Answer 1

A, C, and E are true.

Explanation:

These are all done the same way.

Look at (A). If the statement is true, then 8² + 15² = 17², because the Pythagorean theorem says that if you square the lengths of the two shorter sides of a right angle, their sum will equal the square of the longest side: a² + b² = c².

8² = 64. 15² = 225. So 8² + 15² = 64 + 225 = 289.

So if the statement is true, then 289 = 17².

And yes 17² = 289, so the statement is true.

On the other hand, (B) is false. 7² + 24² = 49 + 576 = 625

But the third side squared, 35² = 1225, not 625.