Question

Penny built a wooden ramp that rose 9 inches over a horizontal distance of 29 inches, as shown below.



image.png



What is the length, to the nearest whole inch, of the ramp's inclined side?

Answer 1

To find the length of the ramp's inclined side, we can use the Pythagorean theorem. The ramp, the horizontal distance, and the vertical rise form a right triangle where:

- The vertical rise (height) is 9 inches.
- The horizontal distance (base) is 29 inches.
- The length of the ramp (hypotenuse) is what we want to calculate.

According to the Pythagorean theorem:

\[
c^2 = a^2 + b^2
\]

where:
- \( c \) is the hypotenuse (length of the ramp),
- \( a \) is one leg of the triangle (vertical rise),
- \( b \) is the other leg of the triangle (horizontal distance).

Substituting the known values into the equation:

\[
c^2 = 9^2 + 29^2
\]
\[
c^2 = 81 + 841
\]
\[
c^2 = 922
\]

Now, we take the square root of both sides to solve for \( c \):

\[
c = \sqrt{922}
\]

Calculating \( \sqrt{922} \):

\[
c \approx 30.34
\]

To find the length of the ramp to the nearest whole inch, we round 30.34 to:

\[
\boxed{30}
\]

Thus, the length of the ramp's inclined side is approximately 30 inches.