Question

A rectangular playground is 420 sq.m. If its length is increases by 7 m and breadth is decreased by 5 metres, the area remains the same. Find the length and breadth of the playground?

Answer 1

Let the length of the rectangular playground is x m. Then, its breadth is $\frac{420}{x}$ m ,as area is given 420 m².
Thus, by the given condition, we get
$$\begin{gathered} \left(x+7\right)\left(\frac{420}{x}-5\right)=420 \\ \Rightarrow \left(x+7\right)\left(420-5x\right)=420x \end{gathered}$$
$\Rightarrow$ 420x –5x² + 2940 –35x = 420x
$\Rightarrow$ 5x² +35x – 2940 = 0
$\Rightarrow$ 5(x² + 7x – 588) = 0
$\Rightarrow$ x² + 7x – 588 = 0
On splitting the middle term 7x as 28x – 21x, we get
$\Rightarrow$ x² + 28x – 21x – 588 = 0
$\Rightarrow$ x(x + 28) – 21(x + 28) = 0
$\Rightarrow$ (x + 28)(x – 21) = 0
$\Rightarrow$ x + 28 = 0 or x – 21 = 0
$\Rightarrow$ x = –28 or x = 21
Since, the length of the playground cannot be negative, so we get x = 21
Thus, the length of the playground is x = 21 m
and the breadth of the playground is $\frac{420}{x}=\frac{420}{21}=20\mathrm{m}.$