Question

The length of a rectangle is increased by 35 % and the width is decreased by 30 %. Calculate the
percentage change in the area of the rectangle. [3 marks]

Answer 1

Step-by-step explanation:

If the length of a rectangle is increased by 20 percent and if it's breadth is decreased by 10 percent. What happen to area of rectangle?

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Let the length & breadth of the original rectangle be x & y respectively. So its area will be xy

Now, the length of the rectangle is increased by 20% i.e. x2=x+20100x=x+15x=65x , & the breadth of the rectangle is decreased by 10% i.e. y2=y−10100y=y−110y=910y . Thus the area of the new rectangle will be x2y2=65x×910y=5450xy=2725xy

Thus, the area of the new rectangle will be 2725 times the area of the original rectangle.

Now let's calculate tge relative percentage increase in the area of the rectangle

A2−A1A1×100=2725xy−xyxy×100=225xyxy×100=225100=8

Thus, there is a total increase of 8% in the area of the original rectangle.

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