Pythagorean Theorem

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 is expressed as: a² + b² = c².

Front

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

Back

The formula to find the length of the hypotenuse (c) is: c = √(a² + b²).

Front

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

Back

The length of the hypotenuse is 5, calculated as: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root.

Front

Is the statement 'a² + b³ = c⁴' true or false?

Back

False. The correct statement is 'a² + b² = c²'.

Front

In a right triangle, if one side is 6 and the hypotenuse is 10, what is the length of the other side?

Back

The length of the other side is 8, calculated as: b = √(10² - 6²) = √(100 - 36) = √64 = 8.

Front

What is the distance across a soccer field that is 90 meters wide and 120 meters long?

Back

The distance is 150 meters, calculated as: c = √(90² + 120²) = √(8100 + 14400) = √22500 = 150.

Front

If a right triangle has sides of length 5 and 12, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 13, calculated as: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

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 equals the square of the longest side (hypotenuse).

Front

If the hypotenuse is 15 and one side is 9, how do you find the other side?

Back

Use the formula: b = √(15² - 9²) = √(225 - 81) = √144 = 12.