The smaller rectangle in the figure

boomgoesthegmat wrote:

The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were each extended by w feet to make the larger rectangular lot shown. If the area of the enlarged lot is twice the area of the original lot, what is the value of w?

A) 25
B) 50
C) 75
D) 100
E) 200

We are given a diagram, which represents a parking lot, with a smaller rectangle inside a larger rectangle. The dimensions of the smaller rectangle are 100 ft. by 150 ft., and the dimensions of the larger rectangle are (100 + w) ft. by (150 + w) ft. Since the area of the larger rectangle is twice that of the smaller rectangle, we can create the following equation:

(w + 100)(w + 150) = 2(100 x 150)

w^2 + 250w + 15,000 = 30,000

w^2 + 250w – 15,000 = 0

(w + 300)(w – 50) = 0

w = -300 or w = 50

Since w must be positive, w must be 50.

Answer: B

Hi ALL,

We're told that the smaller rectangle in the figure above represents the original size of a parking lot before its length and width were each extended by W feet to make the larger rectangular lot shown and the area of the enlarged lot is TWICE the area of the original lot. We're asked for the value of W. This question can be solved by TESTing THE ANSWERS.

To start, the original lot is (100 ft)(150 ft) = 15,000 ft^2, so the larger lot has to be 30,000 ft^2.

Since 30,000 is such a 'round' number, it's likely that (100+W) or (150 + W) will ALSO be a nice 'round' number. The easiest answer among the 5 choices that will lead to that type of round number is 50, so we'll TEST Answer B first:

Answer B: 50
IF.... W=50, then the dimensions of the larger lot will be (150 ft) and (200 ft).
(150 ft)(200 ft) = 30,000 ft
This is an exact match for what we were told, so this MUST be the answer.

Final Answer: B

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