Pythagorean theorem and its applications.

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

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

What is the hypotenuse of a right triangle?

Back

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

Front

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

Back

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

Front

How do you find the area of a square?

Back

The area of a square is found by squaring the length of one of its sides: Area = side².

Front

What is the formula to calculate the area of a right triangle?

Back

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

Front

In a right triangle, if the legs are 8 and 12, what is the length of the hypotenuse?

Back

14.4 (Using the Pythagorean theorem: 8² + 12² = 64 + 144 = 208; √208 ≈ 14.4).

Front

What is the relationship between the diagonal and the sides of a rectangle?

Back

The diagonal of a rectangle can be found using the Pythagorean theorem: diagonal² = length² + width².

Front

If a laptop has a diagonal of 17 inches and a height of 10 inches, how do you find the width?

Back

Use the Pythagorean theorem: width = √(diagonal² - height²) = √(17² - 10²) = √(289 - 100) = √189 ≈ 13.7 inches.