Q. 403.8( 12 Votes )

# The area of a rectangle gets reduced by 67 square metres, when its length is increased by 3 m and breadth is decreased by 4 m. If the length is reduced by 1 m and breadth is increased by 4 m, the area is increased by 89 square metres. Find the dimensions of the rectangle.

Answer :

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

area of rectangle = l×b

According to question -

(l + 3)(b - 4) = (l×b) - 67

⇒ lb - 4l + 3b - 12 = lb - 67

⇒ 4l - 3b = 55.....(1)

and,

(l - 1)(b + 4) = (l×b) + 89

⇒ lb + 4l - b - 4 = lb + 89

⇒4l - b = 93.....(2)

Subtracting Equation (1) From equation (2), we get -

b = 19

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

l = 28

Thus, Length = 28 meters and Breadth = 19 meters.

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