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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

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

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5 cm.

Front

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

Back

The perimeter (P) of a right triangle is the sum of the lengths of all three sides: P = a + b + c.

Front

Calculate the perimeter of a right triangle with legs of 3 cm and 4 cm.

Back

Perimeter = 3 cm + 4 cm + 5 cm = 12 cm.

Front

What is the length of the diagonal of a rectangle with a width of 50 yards and a length of 100 yards?

Back

Using the Pythagorean Theorem: d² = 50² + 100²; d² = 2500 + 10000; d² = 12500; d = 111.8 yards.

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If the lengths of the legs of a right triangle are 5 cm and 12 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12²; c² = 25 + 144; c² = 169; c = 13 cm.

Front

What is the length of the missing side if one leg is 8 cm and the hypotenuse is 10 cm?

Back

Using the Pythagorean Theorem: 10² = 8² + b²; 100 = 64 + b²; b² = 36; b = 6 cm.

Front

What is the area of a right triangle with legs of 6 cm and 8 cm?

Back

Area = (1/2) * base * height = (1/2) * 6 cm * 8 cm = 24 cm².