Question

The length of a rectangular playground is $2m$ longer than its breadth. If the area of the playground is $195m^2$, find the length and breadth of the field.

Answer 1

Given that:

Area of the rectangular playground $=195m^2.$

To find:

Length $=?,$ Breadth $=?$

Solution:

Let breadth of the rectangular playground $=b$

Length of the rectangular playground $=(b+2)$

Area of rectangular playground $=$ Length $\times$ Breadth

$\Rightarrow 195=(b+2)\times b$

$\Rightarrow 195=b^2+2b$

$\Rightarrow b^2+2b-195=0$

$\Rightarrow b^2+15b-13b-195=0$

$\Rightarrow b(b+15)-13(b+15)=0$

$\Rightarrow (b-13)(b+15)=0$

$\Rightarrow b=13$ or $b=-15$

Value $b$ of can't be negative. So $b=13$

Therefore, breadth of the rectangular playground $=13m$

and length of the rectangular playground $=15m$