Chapter 11.1, Problem 27WE

To determine

To Find: The area of path.

Answer to Problem 27WE

  $144m^2$

Explanation of Solution

Given: A path $2m$ wide surround a rectangular garden of $20m$ long and $12m$ wide.

Given:

Length of garden= $20m$

Width of garden= $12m$

Width of path= $2m$

  

Area of path = Area of outer rectangle − area of inner rectangle

Area of outer rectangle $PQRS$

  $\begin{array}{l}length=20+2+2=24m\\ width=12+2+2=16m\\ area=bh\\ A=(24)(16)\\ A=384m^2\end{array}$

Area of inner rectangle $ABCD$

  $\begin{array}{l}A=bh\\ A=(20)(12)\\ A=240m^2\end{array}$

Now area of path

  $\begin{array}{l}{A}_p=384-240\\ A_p=144m^2\end{array}$

Hence, $144m^2$