Pythagorean theorem Review

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

What is the formula to find the length of the diagonal of a rectangle?

Back

The length of the diagonal (d) of a rectangle can be found using the Pythagorean theorem: d = √(length² + width²).

Front

If a rectangle has a length of 8.5 inches and a width of 11 inches, what is the length of the diagonal?

Back

Using the formula: d = √(8.5² + 11²) = √(72.25 + 121) = √193.25 ≈ 13.9 inches.

Front

What is the area of a square with a side length of 5 cm?

Back

The area (A) of a square is calculated as A = side². Therefore, A = 5² = 25 cm².

Front

If the area of a square is 25 in², what is the length of one side?

Back

The length of one side (s) can be found using the formula: s = √(area). Thus, s = √25 = 5 inches.

Front

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

Back

In a right triangle, the lengths of the sides are related by the Pythagorean theorem: the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If one side of a right triangle is 4 feet and the hypotenuse is 13 feet, what is the length of the other side?

Back

Using the Pythagorean theorem: c² = a² + b², we have 13² = 4² + b². Thus, 169 = 16 + b², so b² = 153, and b ≈ 12.37 feet.

Front

What is the area of a square if the side length is 12 inches?

Back

The area (A) is calculated as A = side². Therefore, A = 12² = 144 in².

Front

How do you find the length of a rectangle if you know the width and the diagonal?

Back

Use the Pythagorean theorem: length = √(diagonal² - width²).

Front

What is the area of a square with an area of 169 in²?

Back

The side length of the square is √169 = 13 inches.