Chapter 4.3, Problem 16CYU

To determine

To calculate: The dimensions of the garden when area will be doubled by increasing length and breadth by same amount.

Answer to Problem 16CYU

The dimensions of the garden are $12m\text{ by 9}m$ .

Explanation of Solution

Given information:

The figure,

  

Formula used:

Area of a rectangle with length l and breadth b is the product of its length and breadth.

  $\text{A}=l\times b$

Calculation:

Consider the given figure.

  

Recall that area of a rectangle with length l and breadth b is the product of its length and breadth.

  $\text{A}=l\times b$

So, area of the given rectangular garden will be calculated as,

  $\begin{array}{c}\text{A}=l\times b\\ =9\times 6\\ =54m^2\end{array}$ .

Let the amount of length and breadth increased be x .

Now, increasing the length and breadth by same amount i.e. x , the area is doubled.

So, new dimensions will be calculated as,

  $\begin{array}{c}\left(9+x\right)\left(6+x\right)=2\times 54\\ 54+9x+6x+x^2=108\\ x^2+15x-54=0\\ \left(x-3\right)\left(x+18\right)=0\end{array}$

Therefore, either $x=3\text{ or }x=-18$ and since x cannot be negative; thus, value of x is 3.

New dimensions of the garden are,

  $\begin{array}{c}l=9+3\\ =12m\\ b=6+3\\ =9m\end{array}$

Thus, the dimensions of the garden are $12m\text{ by 9}m$ .