Question

The area of a rectangle gets reduced by 8 $m^2$,when its length is reduced by 5m and its breadth is increased by 3 m.If we increase the length by 3m and breadth by 2m,the area is increased by 74$m^2$.Find the length and breadth of the rectangle.

Answer 1

Suppose length and the breadth of rectangle are l and b respectively.

Then the area of rectangle = lb

Case I: When length is reduced by 5 m and breadth is increased by 3 m.
Then new area of rectangle = (l−5)(b+3)
And according to the question we have;
(l−5)(b+3) = lb−8⇒lb+3l−5b−15 = lb−8
⇒3l−5b = 7 ...(i)

Case II: when length is increased by 3 m and breadth by 2 m
Then new area of rectangle = (l+3)(b+2)
And according to the question we have;
(l+3)(b+2) = lb+74⇒lb+2l+3b+6 = lb+74
⇒2l+3b = 68 ...(ii)

Multiplying (i) by 2 and (ii) by 3 and then subtracting (ii) from (i) we get;
6l−10b−6l−9b = 14−204
⇒−19b = −190
⇒b = 10
Then; from (i) we have;3l = 7+5×10⇒3l = 57⇒l = 19
Therefore length and breadth of rectangle are 19 m and 10 m respectively.