Question

The area of a rectangle gets reduced by 67 square units, if its length is increased by 3 and breadth decreased by 4. If length is reduced by 1 and breadth increased by 4 then the area increases by 89 square units. Find the dimensions of the rectangle.
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Answer 1

SOLUTION:-

Let the length & breadth of the rectangle be x m & y m respectively.

CASE 1️⃣

When length is increased by 3m & breadth is decreased by 4m:

xy -(x+3)(y-4)= 67

=)xy-xy +4x -3y+12= 67

=) 4x-3y= 67-12

=) 4x -3y= 55.................(1)

CASE 2️⃣

When the length is decreased by 1m & breadth is increased by 4m:

(x-1)(y+4)- xy = 89

=) xy + 4x -y-4 -xy = 89

=) 4x - y= 89+4

=) 4x -y= 93................(2)

Now,

Subtracting eq. (1) from (2), we get:

=) 2y= 38

=) y=38/2

=) y= 19

So, putting the value of y in eq. (1), we get:

=) 4x -3(19) = 55

=) 4x - 57 = 55

=) 4x= 55+57

=) 4x= 112

=) x=112/4

=) x= 28

Hence,

⚫Length= 28m

⚫Breadth= 19m.

Hope it helps ☺️

Answer 2

Step-by-step explanation:

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