The area of a rectangle gets reduced by 8 m², when its length is reduced by 5 m and its breadth is increased by 3 m. If we increase the length by 3 m and breadth by 2 m, the area is increased by 74 m². Find the length and the breadth of the rectangle.

Question

Philoid · Accepted Answer

Let the length and breadth of rectangle be l and b meters respectively.

area of rectangle = l×b

According to question -

(l - 5)(b + 3) = (l×b) - 8

⇒ lb + 3l - 5b - 15 = lb - 8

⇒ 3l - 5b = 7.....(1)

and,

(l + 3)(b + 2) = (l×b) + 74

⇒ lb + 2l + 3b + 6 = lb + 74

⇒ 2l + 3b = 68.....(2)

From equation (1), we get -

l = (5b + 7)/3.....(3)

Substituting the value of l in equation (2), we get -

⇒ 19b + 14 = 204

⇒ 19b = 190

⇒b = 10

Substituting the value of b in equation (3), we get -

l = 19

Thus, Length = 19 meters and Breadth = 10 meters.

The area of a rectangle gets reduced by 8 m2, when its length is reduced by 5 m and its breadth is increased by 3 m. If we increase the length by 3 m and breadth by 2 m, the area is increased by 74 m2. Find the length and the breadth of the rectangle.