Question

The area of a rectangle gets reduced by $9$ square units, if its length is reduced by $5$ units and breadth is increased by $3$ units. If we increase the length by $3$ units and the breadth by $2$ units, the area increases by $67$ square units. Find the dimensions of the rectangle.

Answer 1

Let, length $=l$ units

breadth $=$ breadth

Area $=a$ square units

$(a-9)=(l-5).(b+3)...\left(1\right)$

(Area of rectangle $=$ length $\ast$ breadth)

$(a+67)=(l+3)(b+2)...\left(2\right)$

$a=lb...\left(3\right)$

put value of a in eq (1) and (2)

$lb-9=lb+3l-5b-15$

$6=3l-5b....\left(4\right)$

$lb+67=lb+2l+3b+6$

$61=2l+3b...\left(5\right)$

from eq(4) and (5)

$[3l-5b=6]\times 3$

$[2l+3b=61]\times 5$

$9l-15b=18$

$+10l+15b=305$

_____________

$19l=323$

$l=17$ Put value in eq (4)

$b=95units$