If each side of a square is decreased by 17%, then by what percentage does its area decrease ?

A25%

B30.79%

C44.31%

D31.11%

Answer:

Given:

Decrease percent = 17%

Concept used:

Using the concept of percentage

Area of square = (Side)²

Calculation:

Let the original side be 10.

Area of original square = (Side)²

⇒ Original area = 10²

New side = (100 – 17)% of 10

⇒ New side = $\frac{83}{100}\times{10}$

⇒ New side = 8.3

New area = (New side)²

⇒ New area = (8.3)²

⇒ New area = 68.89

Percent decrease in area = (Original area – New area)/(Original area) $\times{100}$

⇒ Percent decrease in area = \frac{(100 – 68.89)}{100}\times{100}

⇒ Percent decrease in area = 31.11%

∴ The percentage decrease in area is 31.11%.

Shortcut Trick

Decreasing(%) in area = - x - x + $\frac{(-x\times-x)}{100}$

Decreasing(%) in area = - 17 - 17 + $\frac{(-17\times-17)}{100}$

⇒ - 34 + 2.89 = - 31.11

∴ The percentage decrease in area is 31.11%

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