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

by Vincen » Wed Jun 24, 2020 2:14 am

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

by [email protected] » Fri Apr 16, 2021 8:06 am
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.