Question

The ladder is placed 7
ft. from the house at the bottom and touches the wall 13
ft. up at the top.

What is the length of the ladder?

Round the answer to the nearest tenth.
A.6.2ft
B.23.2ft
C.14.8ft
D.15.2ft
Best answer

Answer 1

To find the length of the ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ladder, in this case) is equal to the sum of the squares of the other two sides.

Let:
- The distance from the base of the wall to the bottom of the ladder (the horizontal side) = 7 ft
- The height at which the ladder touches the wall (the vertical side) = 13 ft
- The length of the ladder (the hypotenuse) = \( L \)

According to the Pythagorean theorem:

\[
L^2 = (7 \, \text{ft})^2 + (13 \, \text{ft})^2
\]

Calculating the squares:

\[
L^2 = 49 + 169
\]

\[
L^2 = 218
\]

Now taking the square root to find \( L \):

\[
L = \sqrt{218} \approx 14.8 \, \text{ft}
\]

Rounding to the nearest tenth, the length of the ladder is approximately **14.8 ft**.

Therefore, the best answer is **C. 14.8 ft**.