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Standard VI

Mathematics

Area of Square

The length an...

Question

The length and breadth of a square are increased by $30$ % and $20$ % respectively. By what percent is the area of the rectangle so formed exceeds the area of the square?

20

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36

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50

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56

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Solution

The correct option is D $56$ %
Let initial length of square $= 10$
Initial area $= 10^{2}$ $= 100$
New length $= 10 + 30 % o f 10 = 13$
New Breadth $= 10 + 20 % o f 10 = 12$
$∴$ New area of rectangle formed $= 13$ $\times$ $12 = 156$
$%$ increase in area $= \frac{156 - 100}{100} \times 100 = 56$ %

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The length and breadth of a square are increased by 30% and 20% respectively. By what percent is the area of the rectangle so formed exceeds the area of the square?

The correct option is D 56%Let initial length of square =10Initial area =102 =100New length =10+30% of 10=13New Breadth =10+20% of 10=12∴ New area of rectangle formed =13 × 12=156% increase in area =156−100100×100=56%

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