## A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph an

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### A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph an

by BTGmoderatorDC » Mon Oct 03, 2022 5:01 pm

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A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches?

A. 34
B. 36
C. 38
D. 40
E. 42

OA D

Source: GMAT Prep

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### Re: A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograp

by swerve » Sun Oct 09, 2022 8:43 am
BTGmoderatorDC wrote:
Mon Oct 03, 2022 5:01 pm
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches?

A. 34
B. 36
C. 38
D. 40
E. 42

OA D

Source: GMAT Prep
Let Length and Breadth of photograph be $$L$$ and $$B$$ respectively.
Perimeter is given by $$2*(L+b) \qquad (1)$$

According to the question:

$$(L+2)(B+2) = m \qquad (2)$$

and

$$(L+4)(B+4) = m + 52 \longrightarrow (L+4)(B+4) - 52 = m \qquad (3)$$

Equating $$(2)$$ and $$(3)$$

$$(L+2)(B+2) = (L+4)(B+4) - 52$$

$$LB + 2L + 2B + 4 = LB + 4L + 4B + 16 -52$$

Simplify
$$2L + 2B = 40 \longrightarrow 2(L+B) = 40$$ (Check eq $$(1)$$)

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### Re: A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograp

by [email protected] » Fri Dec 09, 2022 9:26 am
BTGmoderatorDC wrote:
Mon Oct 03, 2022 5:01 pm
A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches?

A. 34
B. 36
C. 38
D. 40
E. 42

OA D

Source: GMAT Prep
Solution:

We are given that a rectangular photograph is surrounded by a border that is 1 inch wide on each side and that the total area of the photograph and border is M square inches. If we let L = the length of the photograph and W = the width of the photograph, since the border surrounds the length and width on two sides, the length of the photograph and border is L + 2 and the width of the photograph and border is W + 2.

We can now represent the area of the border and photograph:

area = length x width

M = (L + 2)(W + 2)

M = WL + 2W + 2L + 4

We are also given that if the border had been 2 inches wide on each side, the total area would have been (M + 52) square inches. Thus, the new length of the border and photograph would be L + 4 and the new width of the border and photograph would be W + 4.

The new area of the border and photograph is:

M + 52 = (L + 4)(W + 4)

M + 52 = WL + 4W + 4L + 16

M = WL + 4W + 4L – 36

We have two equations for M. Let’s equate them and simplify:

WL + 2W + 2L + 4 = WL + 4W + 4L – 36

2W + 2L + 4 = 4W + 4L – 36

2W + 2L = 4W + 4L – 40

2W + 2L = 40

Since perimeter = 2L + 2W, the perimeter of the photograph is 40 inches.