Question

Determine whether the given lengths can be sides of a right triangle. Which of the following are true statements?

The lengths 7, 40 and 41 can be sides of a right triangle. The lengths 12, 16, and 20 cannot be sides of a right triangle.

The lengths 7, 40 and 41 cannot be sides of a right triangle. The lengths 12, 16, and 20 cannot be sides of a right triangle.

The lengths 7, 40 and 41 can be sides of a right triangle. The lengths 12, 16, and 20 can be sides of a right triangle.

The lengths 7, 40 and 41 cannot be sides of a right triangle. The lengths 12, 16, and 20 can be sides of a right triangle.

Answer 1

The lengths 7, 40 and 41 cannot be sides of a right triangle. The lengths 12, 16, and 20 can be sides of a right triangle.

You can test this by using the Pythagorean theorem, which states a^2+b^2=c^2
with 7,40 and 41
7^2+40^2 does not equal to 41^2
but with 12,16, and 20
12^2+16^2=20^2
therefore, the last statement is correct.