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Question

The perimeter of a rectangular sheet of paper is 84 cm. If the length of the paper is increased by 3cm and the breadth decreased by 1m, then the area of the paper is increased by 15 $c m^{2}$ . What is the difference in the length and breadth of the original rectangular sheet of paper?

12 m

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15 m

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41 m

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Solution

The correct option is A 12 m
Let the length =l and breadth =b

2(l+b)=84; l+b = 42----------(1)

Area =lb

When changes are made, (l+3)(b-1)= lb + 3b – l – 3

Given that lb + 3b – l –3 = lb +15

3b – l=18--------------------(2)

By solving we get

l=27 and b=15. difference = 12

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The perimeter of a rectangular sheet of paper is 84 cm. If the length of the paper is increased by 3cm and the breadth decreased by 1m, then the area of the paper is increased by 15 cm2. What is the difference in the length and breadth of the original rectangular sheet of paper?

The correct option is A 12 mLet the length =l and breadth =b 2(l+b)=84; l+b = 42----------(1) Area =lb When changes are made, (l+3)(b-1)= lb + 3b – l – 3 Given that lb + 3b – l –3 = lb +15 3b – l=18--------------------(2) By solving we get l=27 and b=15. difference = 12

The perimeter of a rectangular sheet of paper is 84 cm. If the length of the paper is increased by 3cm and the breadth decreased by 1m, then the area of the paper is increased by 15 $c m^{2}$ . What is the difference in the length and breadth of the original rectangular sheet of paper?

The correct option is A 12 m
Let the length =l and breadth =b

2(l+b)=84; l+b = 42----------(1)

Area =lb

When changes are made, (l+3)(b-1)= lb + 3b – l – 3

Given that lb + 3b – l –3 = lb +15

3b – l=18--------------------(2)

By solving we get

l=27 and b=15. difference = 12