The smaller rectangle in the figure above represents the original size of a parking lot before its length and width were

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2015-10-16_0901.png
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

[spoiler]OA=B[/spoiler]

Source: Official Guide

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Vincen wrote:
Wed Jun 24, 2020 2:14 am
2015-10-16_0901.png

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

[spoiler]OA=B[/spoiler]

Source: Official Guide
Solution:

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 area 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

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