Question

The area of a rectangle increases by $200m^2$, if the length is increased by $8$ m and the breadth by $3$ m. The area increases by $255m^2$, if the length is increased by $3$ m and breadth by $8$ m. Find the length and the breadth of the rectangle.

• A. $l=4$ m, $b=4$ m
• B. $l=24$ m, $b=13$ m
• C. $l=13$ m, $b=18$ m
• D. $l=21$ m, $b=8$ m

Answer 1

The correct option is B $l=24$ m, $b=13$ m

Let the numbers be $x$ and $y$:

Given, $(x+8)(y+3)=200+xy$ ....(1)

and $(x+3)(y+8)=255+xy$ ....(2)

Simplifying the $2$ equations, we get

$3x+8y=176$

$3y+8x=231$

$x=\frac{(-8y+176)}{3}$

Substituting this value of $x$ in any equation, we get

$3y+8\frac{(-8y+176)}{3}=231$

Thus, $x=24$ and $y=13$.

Therefore, length is $24$ m and breadth $=13$ m.