Chapter 1.7, Problem 34E

Solution

To calculate the lengths of the four sections for the installation of rain gutter.

  $\text{26 ft, 26 ft, }42\text{ ft}$ and $42\text{ ft}$ are the lengths of four sections to install the rain gutter around the rectangular house.

Given: Perimeter of the house $=136\text{ ft}$

Formula used : Perimeter of the rectangle $=2\left(\text{length}+\text{width}\right)$

Calculation : Let the width of the rectangular house $=x\text{ ft}$

And, from the given information, the length of the rectangular house is $\text{16 ft}$ more than the width of the rectangular house. Hence, the length of rectangular house $=\left(x+16\right)\text{ft}$

Now, the perimeter of the rectangular house is given by:

  $\begin{array}{l}P=2\left(length+width\right)\\ \Rightarrow 136=2\left(x+16+x\right)\\ \Rightarrow \frac{136}{2}=2x+16\\ \Rightarrow 2x=68-16\\ \Rightarrow x=\frac{52}{2}\\ \Rightarrow x=26\text{ ft}\end{array}$

Hence, the length of the rectangular house is $26\text{ ft}$ and the width of the rectangular house is $(x+16)=26+16=42\text{ ft}\text{.}$ Therefore, the lengths of the four sections for the rain gutter installation are $26\text{ ft,}$ $26\text{ ft,}$ $42\text{ ft}$ and $42\text{ ft}\text{.}$