Question

7.

The length of a rectangle is increased by 10% while its breadth is decreased by 10%.
Determine, if any, the percentage change in its area.
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Answer 1

the new area is 1% smaller.

Explanation:

the area of a rectangle is length times breadth.

let's call them a and b

Area = a × b

now, a is increased by 10%. that means it is multiplied by 11/10.

because 100% means the whole thing, 1% means a 1/100th part of the whole. and 10% then means 10 times the 1/100th part of 10 × 1/100 = 10/100 = 1/10

if then simmering increases by 10% it means that it is the original 100% plus 10%.

so, it is 100/100 + 10/100 = 10/10 + 1/10 = 11/10

therefore the new length is

a(new) = a(old)×11/10

in exactly the same way, when the breadth is reduced by 10% we get then

breadth(new) = breadth(old)×9/10

so, Area(new) = a(new)×b(new) = a(old)×11/10 × b(old)×9/10

remember, Area(old) = a(old)×b(old)

so, Area(new) = a(old)×b(old) × 11/10 × 9/10 =

= Area(old) × 11/10 × 9/10 =

= Area(old) × 99/100

that means the new area has lost compared to the old area 1/100th of its size. 1/100th = 1%