Question

Sides AB and DC of the rectangle are increased in length by 50% and sides AD and BC are decreased in length by 50%. What is the percentage change in the AREA of the rectangle? A) -50% B) -25% C) 0% D) +25% E) +50%

Answer 1

The percentage of change in the area of the rectangle is -25% ⇒ B

Step-by-step explanation:

The given is:

• Sides AB and DC of the rectangle are increased in length by 50%
• Sides AD and BC are decreased in length by 50%

We need to find the percentage change in the AREA of the rectangle

Assume that the length of AB ans DC is x units, and the length of AD and BC is y units

∵ The length of the sides AB and DC increased by 50%

∵ The length of AB and CD = x

- That means x will increase by 50% of x

∵ 50% of x = (50 ÷ 100) × x = 0.5 x

∴ The length is increased by 0.5 x

∴ The new length of AB and CD = x + 0.5 x = 1.5 x units

∵ The length of the sides BC and AD decreased by 50%

∵ The length of BC and AD = y

- That means y will decrease by 50% of y

∵ 50% of y = (50 ÷ 100) × y = 0.5 y

∴ The length is decreased by 0.5 y

∴ The new length of BC and AD = y - 0.5 y = 0.5 y units

∵ The area before the change = x × y = xy units²

∵ The area after the change = 1.5 x × 0.5 y = 0.75 xy units²

∵ The new area is less than the old area

∴ The area is decreased

- To find the the percentage of change in the area subtract the

   new area from the old area and divide the difference by the

    old area and then multiply the quotient by 100%

∴ The percentage of the change = $\frac{xy-0.75xy}{xy}$ × 100%

∴ The percentage of the change = $\frac{0.25xy}{xy}$ × 100%

∴ The percentage of the change = 0.25 × 100%

∴ The percentage of the change = 25%

∴ The area of the rectangle is decreased by 25% ⇒ (-25%)

The percentage of change in the area of the rectangle is -25%

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