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

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

Back

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

Front

What is the square root of 25?

Back

The square root of 25 is 5.

Front

In the Pythagorean Theorem, what do the letters a, b, and c represent?

Back

In the Pythagorean Theorem, 'a' and 'b' represent the lengths of the legs of the triangle, while 'c' represents the length of the hypotenuse.

Front

What is the perimeter of a right triangle with legs of 3 cm and 4 cm?

Back

The perimeter is the sum of all sides: 3 + 4 + 5 = 12 cm.

Front

What is the area of a right triangle with legs of 3 cm and 4 cm?

Back

The area is calculated as: (1/2) * base * height = (1/2) * 3 * 4 = 6 cm².

Front

Which side is the hypotenuse in a triangle with sides 6, 6.7, and 3?

Back

The hypotenuse is 6.7.

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse is c = √(a² + b²).

Front

If a right triangle has a hypotenuse of 10 and one leg of 6, what is the length of the other leg?

Back

Using the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8.