Michigan Residential Builders License Practice Test

What formula is used to determine the unknown length of a triangle?

1. a^2 + b^2 = c^2

2. l = w × h

3. Area = 1/2 × base × height

4. Pythagorean theorem: a + b + c

The correct answer is: a^2 + b^2 = c^2

The formula a² + b² = c² is fundamental in geometry, particularly pertaining to right triangles. This relationship expresses the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (often referred to as legs) equals the square of the length of the longest side (the hypotenuse). When trying to determine the unknown length of a triangle, especially in the context of a right triangle, this theorem is particularly useful. For example, if you know the lengths of the two legs, you can use the formula to find the hypotenuse. Similarly, if you know the length of one leg and the hypotenuse, you can rearrange the formula to solve for the unknown leg. The other options provided do not directly address determining the lengths of the sides of a triangle. For instance, the formula for area (Area = 1/2 × base × height) calculates the area of a triangle, while the formula l = w × h addresses the area of a rectangle. The mention of a + b + c as a statement doesn’t correctly refer to any established theorem or relationship in this context, as it doesn’t provide a method for finding lengths