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 can be expressed as: a² + b² = c².

Front

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

Back

c = 13 (using the Pythagorean Theorem: 5² + 12² = c², which simplifies to 25 + 144 = 169, thus c = √169 = 13).

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 formula: d = √(width² + height²).

Front

What is the length of the diagonal of a piece of paper that is 11 inches tall and 8 inches wide?

Back

The diagonal length is approximately 13.6 inches (using the formula: d = √(8² + 11²) = √(64 + 121) = √185).

Front

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

Back

The formula is a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Front

If a rectangular monitor is 30 cm wide and 24 cm high, what is its diagonal size?

Back

The diagonal size is approximately 38 cm (using the formula: d = √(30² + 24²) = √(900 + 576) = √1476).

Front

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

Back

In a right triangle, the relationship between the lengths of the sides is defined by the Pythagorean Theorem: a² + b² = c².

Front

Which equation can be used to find the width of a TV that is 40 inches diagonally and 30 inches high?

Back

The equation is 30² + b² = 40².

Front

What does the term 'hypotenuse' refer to in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

What is the value of c if a = 8 and b = 15?

Back

c = 17 (using the Pythagorean Theorem: 8² + 15² = c², which simplifies to 64 + 225 = 289, thus c = √289 = 17).