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 the formula to find the length of the hypotenuse in a right triangle?

Back

The formula to find the length of the hypotenuse (c) is: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

If one side of a right triangle is 15 inches and the hypotenuse is 25 inches, what is the length of the other side?

Back

Using the Pythagorean Theorem: c² = a² + b², we have 25² = 15² + b². Therefore, b = √(25² - 15²) = √(625 - 225) = √400 = 20 inches.

Front

What are the conditions for a triangle to be a right triangle?

Back

A triangle is a right triangle if one of its angles measures 90 degrees and it satisfies the Pythagorean Theorem.

Front

How can you determine if a set of three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

Front

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

Back

In a 3-4-5 triangle, the lengths of the sides satisfy the Pythagorean Theorem: 5² = 3² + 4², which is 25 = 9 + 16.

Front

What is the length of the diagonal of a rectangle with a width of 15 inches and a length of 20 inches?

Back

Using the Pythagorean Theorem: d = √(length² + width²) = √(20² + 15²) = √(400 + 225) = √625 = 25 inches.

Front

If the lengths of two sides of a right triangle are 6 and 8, what is the length of the hypotenuse?

Back

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

Front

What is the value of c in the equation 12² + b² = c² if b = 5?

Back

c = √(12² + 5²) = √(144 + 25) = √169 = 13.

Front

Can the lengths 8, 15, and 17 form a right triangle?

Back

Yes, because 17² = 8² + 15² (289 = 64 + 225).