Pythagorean Theorem all sides

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). Formula: a² + b² = c².

Front

If a = 3 and b = 4, what is c?

Back

c = 5 (Using the Pythagorean Theorem: 3² + 4² = c² => 9 + 16 = c² => c² = 25 => c = 5).

Front

What is the length of the hypotenuse if a = 8 and b = 6?

Back

c = 10 (Using the Pythagorean Theorem: 8² + 6² = c² => 64 + 36 = c² => c² = 100 => c = 10).

Front

If c = 13 and a = 5, what is b?

Back

b = 12 (Using the Pythagorean Theorem: 5² + b² = 13² => 25 + b² = 169 => b² = 144 => b = 12).

Front

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

Back

In a right triangle, the sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse).

Front

If a = 7 and c = 25, what is b?

Back

b = 24 (Using the Pythagorean Theorem: 7² + b² = 25² => 49 + b² = 625 => b² = 576 => b = 24).

Front

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

Back

To find the length of a side, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a².

Front

If a = 12 and b = 16, what is c?

Back

c = 20 (Using the Pythagorean Theorem: 12² + 16² = c² => 144 + 256 = c² => c² = 400 => c = 20).

Front

What is the value of c if a = 9 and b = 12?

Back

c = 15 (Using the Pythagorean Theorem: 9² + 12² = c² => 81 + 144 = c² => c² = 225 => c = 15).

Front

If a = 5 and b = 12, what is c?

Back

c = 13 (Using the Pythagorean Theorem: 5² + 12² = c² => 25 + 144 = c² => c² = 169 => c = 13).