Chapter 12.6, Problem 8P

To determine

To find: the dimension of the new garden.

Answer to Problem 8P

The dimension of new garden is $l=17m\&b=15m$ where $l$ is length and $b$ is breadth.

Explanation of Solution

Given information:

The length of rectangular garden is $14m$ and breadth is $12m$ and Holly wants to increase the area to $255m^2$ .

Formula:

Area of rectangular is $l\times b$ where $l$ is length and $b$ is breadth.

Calculation:

Consider the increased amount in the length and breadth of new rectangle be $x$ .

Then as mentioned above that length of rectangular garden is $14m$ and breadth is $12m$ .

Holly wants to increase the area to $255m^2$ by increase in same amount of length and breadth.

Therefore new length will be as $\left(14+x\right)$ and new breadth will be as $\left(12+x\right)$ .

Recall that area of rectangular is $l\times b$ where $l$ is length and $b$ is breadth.

Therefore the new area of rectangle will be $255=\left(14+x\right)\left(12+x\right)$ .

Therefore

  $\begin{array}{l}255=\left(14+x\right)\left(12+x\right)\Rightarrow 255=x^2+26x+168\Rightarrow x^2+26x-87=0\\ \Rightarrow x^2+29x-3x-87=0\Rightarrow x\left(x+29\right)-3\left(x+29\right)=0\Rightarrow \left(x-3\right)\left(x+29\right)=0\\ \Rightarrow x=3,-29.\end{array}$

Therefore the new dimension of the rectangular garden will be $\left(14+x\right)\Rightarrow 14+3=17$ and $\left(12+x\right)\Rightarrow 12+3=15$ .

Therefore the dimension of new garden is $l=17m\&b=15m$ where $l$ is length and $b$ is breadth.

Here we reject the $x=-29$ as the dimension cannot be in negative.