Pythagorean 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: a² + b² = c².

Front

What are the conditions for a set of three lengths to form a right triangle?

Back

For three lengths to form a right triangle, they must satisfy the Pythagorean Theorem: a² + b² = c², where c is the longest side.

Front

Given the sides 9, 40, and 41, do they form a right triangle?

Back

Yes, they form a right triangle because 9² + 40² = 41² (81 + 1600 = 1681).

Front

How do you calculate the length of the diagonal of a rectangle?

Back

To calculate the diagonal (d) of a rectangle with length (l) and width (w), use the formula: d = √(l² + w²).

Front

What is the length of the diagonal of a pool measuring 25 m by 50 m?

Back

The diagonal is 55.9 m, calculated using the formula: d = √(25² + 50²) = √(625 + 2500) = √3125.

Front

Do the sides 20 m, 8 m, and 19 m form a right triangle?

Back

No, they do not form a right triangle because 20² + 8² ≠ 19² (400 + 64 ≠ 361).

Front

Do the sides 15 cm, 8 cm, and 17 cm form a right triangle?

Back

Yes, they form a right triangle because 15² + 8² = 17² (225 + 64 = 289).

Front

What is the formula to find the missing side of a right triangle?

Back

To find the missing side, use the Pythagorean Theorem: if one side is missing, rearrange the formula: c² - a² = b² or c² - b² = a².

Front

If one side of a right triangle is 6.4 and the other side is 9, what is the length of the hypotenuse?

Back

The hypotenuse is 11.4, calculated using the formula: c = √(6.4² + 9²) = √(40.96 + 81) = √121.96.

Front

What is a right triangle?

Back

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