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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?

(A) 25%
(B) 36%
(C) 50%
(D) 56%
(E) 60%

答案和解析

答案：D

解析：

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 + ((20/100)*l) = 1.2*l and W = w + ((30/100)*w) = 1.3*w

So, the new area will be:

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

1.56*(l*w) = (l*w) + ((56/100)*(l*w))where (l*w) is the original area of the rectangle.So the area is increased by 56%.