Pythagorean Theorem Test Review

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

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

Back

5 cm (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

Front

What is the length of the missing side if c² = 100 and b = 60?

Back

80 (Using the Pythagorean Theorem: c² = a² + b², so 100 = a² + 60², thus a² = 100 - 3600 = 6400, so a = √6400 = 80).

Front

In a right triangle, if the hypotenuse is 13 cm and one side is 5 cm, what is the length of the other side?

Back

12 cm (Using the Pythagorean Theorem: 13² = 5² + b², so 169 = 25 + b², thus b² = 144, so b = √144 = 12).

Front

What are the lengths of the sides of a right triangle if they are 9, 12, and 15?

Back

They form a right triangle (9² + 12² = 15², 81 + 144 = 225).

Front

If a right triangle has legs of lengths 8 cm and 15 cm, what is the length of the hypotenuse?

Back

17 cm (Using the Pythagorean Theorem: 8² + 15² = 64 + 225 = 289, so c = √289 = 17).

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 c² = 49 and a = 7, what is the length of b?

Back

0 (Using the Pythagorean Theorem: 49 = 7² + b², so 49 = 49 + b², thus b² = 0, so b = 0).

Front

What is the length of the hypotenuse if one side is 6 cm and the other side is 8 cm?

Back

10 cm (Using the Pythagorean Theorem: 6² + 8² = 36 + 64 = 100, so c = √100 = 10).

Front

If a right triangle has sides of lengths 5 cm, 12 cm, and 13 cm, is it a right triangle?

Back

Yes, it is a right triangle (5² + 12² = 13², 25 + 144 = 169).