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Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

The length of a rectangle is increased by 20%, and the width of the rectangle is increased by 30%. By what percentage will the area of the rectangle be increased?

Answer Choices

Right! (Applause.)

Explanation

Let l and w be the original length and width of the rectangle, respectively. If we denote by L and W the new length and width of the rectangle, respectively, then we have:

L = l + ((20 over 100) times l) = 1.2 times l and W = w + ((30 over 100) times w) = 1.3 times w

So, the new area will be:

A = L times W = (1.2 times l) times (1.3 times w) = 1.56 times (l times w)

1.56 times (l times w) = (l times w) + ((56 over 100) times (l times w))


where (l times w) is the original area of the rectangle.
So the area is increased by 56%.

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