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Question

The area of a rectangle remains the same if the length is increased by 7 meters and the breadth is decreased by 3 meters. The area remains unaffected if the length is decreased by 7 meters and breadth in increased by 5 meters. Find the dimensions of the rectangle.

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Solution

Let the length and breadth of the rectangle be and units respectively

Then, area of rectangle =square units

If length is increased by meters and breadth is decreased by meters when the area of a rectangle remains the same

Therefore,

If the length is decreased by meters and breadth is increased by meters when the area remains unaffected, then

Thus we get the following system of linear equation

By using cross-multiplication, we have

and

Hence, the length of rectangle ismeters

The breadth of rectangle is meters


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