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: a² + b² = c².

Front

What is a right triangle?

Back

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

Front

What is the hypotenuse of a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

If one leg of a right triangle is 3 feet and the other leg is 4 feet, what is the length of the hypotenuse?

Back

5 feet (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

How do you find the length of one leg of a right triangle if you know the hypotenuse and the other leg?

Back

You can rearrange the Pythagorean Theorem: a² = c² - b², where c is the hypotenuse and b is the known leg.

Front

What is the formula to calculate the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.

Front

In a ladder problem, if the ladder is 15 feet long and reaches a height of 12 feet, how far is the base of the ladder from the wall?

Back

9 feet (using the Pythagorean Theorem: 15² = 12² + b²; 225 = 144 + b²; b² = 81; b = 9).

Front

What is the relationship between the sides of a 5-12-13 triangle?

Back

The sides 5, 12, and 13 form a right triangle, satisfying the Pythagorean Theorem: 5² + 12² = 13².

Front

What is the significance of the Pythagorean Theorem in real-life applications?

Back

The Pythagorean Theorem is used in various real-life situations, such as construction, navigation, and determining distances.

Front

If a right triangle has legs of lengths 8 feet and 15 feet, what is the length of the hypotenuse?

Back

17 feet (using the Pythagorean Theorem: 8² + 15² = 64 + 225 = 289; √289 = 17).