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

If one leg of a right triangle is 8 and the other leg is 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 8² + 12² = 64 + 144 = 208. Therefore, c = √208 ≈ 14.4.

Front

In a right triangle, if the legs are 6 and 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100. Therefore, c = √100 = 10.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the side opposite the right angle is the hypotenuse, and it is always the longest side. The other two sides are called legs.

Front

How do you find the length of a missing leg in a right triangle?

Back

To find a missing leg (a or b), rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a².

Front

What is the formula to calculate the diagonal of a square?

Back

The diagonal (d) of a square can be calculated using the formula: d = a√2, where a is the length of a side of the square.

Front

If the area of a square is 81 square centimeters, what is the length of one side?

Back

The length of one side (a) can be found by taking the square root of the area: a = √81 = 9 cm.

Front

What is the height of a right triangle?

Back

The height of a right triangle is the perpendicular distance from the base to the opposite vertex.

Front

In a right triangle, if the height is 6 feet and the base is 8 feet, what is the length of the hypotenuse?

Back

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

Front

What is an isosceles triangle?

Back

An isosceles triangle is a triangle that has at least two sides of equal length.