Pythagorean Theorem Practice with 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

How do you calculate the diagonal of a rectangle using the Pythagorean Theorem?

Back

To find the diagonal (d) of a rectangle, use the formula: d = √(width² + height²).

Front

If a right triangle has legs of lengths 6 inches and 8 inches, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10 inches.

Front

What is the length of the diagonal of a laptop screen that is 10 inches wide and 8 inches high?

Back

Using the Pythagorean Theorem: d = √(10² + 8²) = √(100 + 64) = √164 ≈ 12.81 inches, rounded to 13 inches.

Front

In a right triangle, if one leg is 9 inches and the hypotenuse is 15 inches, what is the length of the other leg?

Back

Using the Pythagorean Theorem: b = √(15² - 9²) = √(225 - 81) = √144 = 12 inches.

Front

What is the distance between two corners of a soccer field that is 90 meters wide and 120 meters long?

Back

Using the Pythagorean Theorem: d = √(90² + 120²) = √(8100 + 14400) = √22500 = 150 meters.

Front

If a right triangle has a hypotenuse of 13 inches and one leg of 5 inches, how do you find the other leg?

Back

Use the Pythagorean Theorem: b = √(13² - 5²) = √(169 - 25) = √144 = 12 inches.

Front

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

Back

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

Front

If the legs of a right triangle are 7 cm and 24 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(7² + 24²) = √(49 + 576) = √625 = 25 cm.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where the shortest side is opposite the 30° angle.