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: c² = a² + b².

Front

What is a right triangle?

Back

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

Front

What is the hypotenuse in 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 cm and the other leg is 4 cm, what is the length of the hypotenuse?

Back

5 cm (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

How do you find the length of one leg of a right triangle if you know the hypotenuse and the other leg?

Back

You can rearrange the Pythagorean Theorem: a² = c² - b², where c is the hypotenuse and b is the known leg.

Front

What is the area of a square with a side length of 9 ft?

Back

The area is 81 ft² (Area = side² = 9² = 81).

Front

If a ladder is 10 feet long and the base is 4 feet from the wall, how high does it reach on the wall?

Back

9 feet (using the Pythagorean Theorem: 10² = 4² + height²; 100 = 16 + height²; height² = 84; height = √84 ≈ 9).

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

It is a special case of a right triangle where the sides are in the ratio 3:4:5, satisfying the Pythagorean Theorem.

Front

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

Back

The perimeter is the sum of all three sides: P = a + b + c.

Front

If a triangle has a hypotenuse of 12 cm and one leg of 10 cm, what is the length of the other leg?

Back

6.6 cm (using the Pythagorean Theorem: 12² = 10² + b²; 144 = 100 + b²; b² = 44; b = √44 ≈ 6.6).