Austen is building a wheelchair ramp onto his porch. If the ramp begins 68 centimeters from the porch and is 85 centimeters long, how tall is the porch?

To solve this problem, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

In this case, the length of the ramp is the hypotenuse (c), the distance from the porch is one side (a), and the height of the porch is the other side (b) that we are trying to find.

Given: a = 68 cm (distance from the porch) c = 85 cm (length of the ramp)

We can rearrange the Pythagorean theorem to solve for b (the height of the porch):

b² = c² - a² b² = (85 cm)² - (68 cm)² b² = 7225 cm² - 4624 cm² b² = 2601 cm²

To find b, we take the square root of b²:

b = √2601 cm² b = 51 cm

So, the porch is 51 centimeters tall.