Pythagorean Theorem Word Problems

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: c² = a² + b².

Front

In a right triangle, what are the legs?

Back

The legs of a right triangle are the two sides that form the right angle. They are usually referred to as sides a and b.

Front

If one leg of a right triangle is 6 feet and the other leg is 8 feet, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10 feet.

Front

What is the length of the diagonal of a rectangle that is 3 feet tall and 6 feet wide?

Back

Using the Pythagorean Theorem: c² = 3² + 6²; c² = 9 + 36; c² = 45; c = √45 ≈ 6.7 feet.

Front

True or False: The hypotenuse is always the longest side of a right triangle.

Back

True.

Front

What is the formula to find the length of the hypotenuse in a right triangle?

Back

The formula is c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the legs.

Front

If the hypotenuse of a right triangle is 13 feet and one leg is 5 feet, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 13² = 5² + b²; 169 = 25 + b²; b² = 144; b = 12 feet.

Front

What does it mean if a triangle is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

In the context of the Pythagorean Theorem, what is a 'leg'?

Back

A leg is one of the two sides of a right triangle that are not the hypotenuse.

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, because 25² = 7² + 24² (625 = 49 + 576).