Question

R is a rectangle If its length and breadth are both increased by y cm its area would increase by 32 cm${}^2$
If its length and breadth are both decreased by y cm its area would decrease by 24 cm${}^2$. Find y

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Let the length be $l$ and breadth be $b$
Then Area of the rectangle $A=length\times breadth=l\times b$
As per the given statements,
$A+32=(l+y)\times (b+y)$
$=>A+32=lb+ly+by+y^2$
$=>A+32=A+ly+by+y^2$
$=>32=ly+by+y^2$ -- (1)
Also, $A-24=(l-y)\times (b-y)$
$=>A-24=lb-ly-by+y^2$
$=>A-24=A-ly-by+y^2$
$=>-24=-ly-by+y^2$ -- (2)
Adding equations, 1 and 2, we get
$8=2y^2$
$=>y^2=4$
$=>y=2$