Chapter 11.1, Problem 32WE

To determine

To Find: The total perimeter.

Answer to Problem 32WE

  $132cm$

Explanation of Solution

Given: The length of the sides of three squares are $s,s+1,s+2$ and the total area is $365c{m}^2$ .

Given: sides= $s,s+1,s+2$

Area= $365c{m}^2$

The side of first square= $s$

Area= $s^2$

The side of second square= $s+1$

Area= ${(s+1)}^2$

The side of third square= $s+2$

Area= ${(s+2)}^2$

Now

Total area

  $\begin{array}{l}$ 365=s^2+{(s+1)}^2+{(s+2)}^2$365=s^2+s^2+1+2s+s^2+4+4s\\ 365=3s^2+6s+5\\ 3s^2+6s-360=0\\ (s-10)(s+12)=0\\ s=10\end{array}$

Side of the square is $10cm$

Now

Total perimeter

  $\begin{array}{l}P=4s+4(s+1)+4(s+2)\\ P=4(10)+4(11)+4(12)\\ P=132cm\end{array}$

Hence, total perimeter is $132cm$