Chapter 6, Problem 10CCSR

To determine

To find the fencing that I need, if M used 400 ft of fencing to enclose a rectangular area in his backyard and I wants to enclose similar area with two times of length and width.

Answer to Problem 10CCSR

800 ft& option F is correct.

Explanation of Solution

Given information:

M used 400 ft of fencing to enclose a rectangular area in his backyard and Iwants to enclose similar area with two times of length and width.

Calculation:

Let $l\&w$ be the length and width of M’s rectangular area in his backyard respectively.

Then the length and width of I rectangular area is $2l\&2w$ respectively.

Now given that the perimeter of M’s rectangular area in his backyard is 400 ft. That is,

  $\begin{array}{l}2\left(l+w\right)=400\\ \Rightarrow l+w=200\to \left(1\right)\end{array}$

Now the perimeter of I rectangular area is,

  $\begin{array}{l}2\left(2l+2w\right)=2\left[2\left(l+w\right)\right]\\ =4\left(l+w\right)\\ =4\left(200\right)\left[\text{Using}\text{equation}\left(\text{1}\right)\right]\\ =800\text{ft}\end{array}$

Hence option F is correct.