Pythagorean Theorem Test 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

How do you find the length of the diagonal of a rectangle?

Back

To find the length of the diagonal (d) of a rectangle, use the Pythagorean Theorem: d = √(length² + width²).

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

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

Front

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

Back

The area of a square is calculated as side². Therefore, area = 5² = 25 in².

Front

If the area of a square is 36 in², what is the length of one side?

Back

To find the side length, take the square root of the area: side = √36 = 6 in.

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. The shortest side is opposite the 30° angle.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

How do you calculate the area of a right triangle?

Back

The area of a right triangle is calculated as: Area = (1/2) × base × height.

Front

If a rectangle has a width of 4 feet and a diagonal of 13 feet, how do you find the length?

Back

Use the Pythagorean Theorem: length = √(diagonal² - width²) = √(13² - 4²) = √(169 - 16) = √153 ≈ 12.37 ft.

Front

What is the formula for the perimeter of a rectangle?

Back

The perimeter (P) of a rectangle is calculated as: P = 2 × (length + width).