Question

The length of a rectangular blackboard is $8cm$ more than its breadth. If its length is increased by $7cm$ and breadth is decreased by $4cm$, its area remains unchanged. Find the length and breadth of the rectangular blackboard.

• A. $28cm,20cm$
• B. $20cm,24cm$
• C. $24cm,16cm$
• D. $28cm,16cm$

Answer 1

The correct option is A $28cm,20cm$

Let the length be $L$ and breadth be $B$
Given, $L=8+B$
Area of the board, $L\times B=(8+B)\times B$
Given, If its length is increased by $7cm$ and breadth is decreased by $4cm$, its area remains unchanged.
$\Rightarrow (L+7)(B-4)=L\times B$
But $L=8+B$
$\Rightarrow (8+B+7)(B-4)=(8+B)\times B$
$\Rightarrow (15+B)(B-4)=(8+B)\times B$
$\Rightarrow 15B-60+B^2-4B=8B+B^2$
$3B=60$
$B=20cm$
So, Length $=20+8=28cm$