Question

If the length of a rectangle is reduced by $5$ units and its breadth in increased by $3$ units then the area of the rectangle is reduced by $8$ square units. If length is reduced by $3$ units and breadth is increased by $2$ units, then the area of rectangle will increase by $67$ square units. Then find the length and breadth of the rectangle.

Answer 1

Length of rectangle is reduced by 5 units and

its breadth is increased by 3 units and the

area of rectangle is reduced by 8 sq. units

$(L-5)(W+3)=LW-8$

$LW+3L-5W-15=LW-8$

$3L-5W=7$ __(1)

Length is reduced by 3 units and breadth is increased

by 2 units, then the area of Rectangle will be

67 sq. units increased

$(L-3)(W+2)=LW+67$

$LW+2L-3W-6=LW+67$

$2L-3W=73$ __(2)

Solving $\left(1\right)\times 2$ by $\left(2\right)\times 3$

$2(3L-5W=7)\to 6L-10W=14$

$3(2L-3W=73)\to 6L-9W=219$

$-W=-205$

$W=205$

W = 205 in eq (1).

$3L-5\left(205\right)=7$

$3L=7+1025$

$3L=1032\to L=\frac{1032}{3}$

$L=344$