Question

Gerry plans to place a 25-foot ladder against the side of his house to clean his gutters. The bottom of the ladder will be 5 feet from the house. How for up the side of the house will the ladder reach?

Short answer

The length of the side of house when ladder reaches is 24.4 feet.

Step-by-step solution

Step 1. Given Information

The ladder's length is 25 foot and ladder's bottom is 5 feet from house.

Step 2. Pythagoras theorem

Let's take house's length till ladder as x feet. On applying the Pythagoras theorem,

$$\begin{gathered} {\mathrm{Base}}^2+{\mathrm{height}}^2={\mathrm{Hypotenuse}}^2 \\ {5}^2+{\left(\mathrm{x}\right)}^2={25}^2 \\ 25+{\mathrm{x}}^2=625 \\ {\mathrm{x}}^2=600 \\ \mathrm{x}=10\sqrt{6} \\ \mathrm{x}=10\times 2.44=24.4 \end{gathered}$$

The length of the side till ladder reaches 24.4 feet.