Question

The length of a rectangle exceeds its Breadth by $9cm$. If the length and breadth are each increased by $3cm$. The area of the new rectangle will be $84c{m}^2$ more than that of the given rectangle. Find the length and breadth of the given rectangle check your solution.

Answer 1

$l=b+9$

Area of rectangle $=l\times b=b(b+9)$

Now,

$l^{\prime }=l+3=b+9+3=b+12$

$b^{\prime }=b+3$

Area of new rectangle $=l^{\prime }\times b^{\prime }$

$b(b+9)+84=(b+3)(b+12)$

$b^2+9b+84=b^2+3b+12b+36$

$6b+36=84$

$\Rightarrow b=\frac{84-36}{6}=\frac{48}{6}=8cm$

$\therefore l=b+9=8+9=17cm$