Chapter 4.8, Problem 29P

To determine

To find how wide should the border be ?

Answer to Problem 29P

Width of the border be 2.5 meters.

Explanation of Solution

Given information: The garden plot 5m by 15m has one of its longer sides next to the wall. The area of the plot is to be provided by digging up a strip of uniform width along the other three sides.

Calculation: The required solution is obtained as,

Area of original garden is $15\times 5=75m^2$ .

For new plot,

Let, Width be $5+D$

Length be $15+2D$

Area of new plot = $150m^2$ (twice the original plot)

  $\begin{array}{l}\left(5+D\right)\left(15+2D\right)=150\\ 75+25D+2D^2=150\\ 2D^2+25D-75=0\\ \left(2D-5\right)\left(D+15\right)=0\\ D=2.5,-15\end{array}$

Ignore negative value.

  $D=2.5$ meters

Hence, Width of the border be 2.5 meters.