Question

perry is building a wheelchair ramp onto his porch. if the ramp begins 32 inches from the porch and is 40 inches long, how tall is the porch? inches

Explanation:

Step1: Identify the triangle type

The ramp, the distance from the porch, and the porch height form a right triangle. The ramp is the hypotenuse (\(c = 40\) inches), the distance from the porch is one leg (\(a = 32\) inches), and the porch height is the other leg (\(b\)). Use the Pythagorean theorem: \(a^2 + b^2 = c^2\).

Step2: Rearrange the formula

Solve for \(b\): \(b^2 = c^2 - a^2\). Substitute \(c = 40\) and \(a = 32\): \(b^2 = 40^2 - 32^2\).

Step3: Calculate the squares

\(40^2 = 1600\), \(32^2 = 1024\). So \(b^2 = 1600 - 1024 = 576\).

Step4: Find the square root

\(b = \sqrt{576} = 24\).

Answer:

24