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Border of photograph

This topic has 3 expert replies and 1 member reply
zeza Junior | Next Rank: 30 Posts
Joined
11 Jun 2012
Posted:
15 messages

Border of photograph

Post Sun Dec 30, 2012 4:13 am
A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?

(A) 3
(B) 4
(C) 6
(D) 8
(E) 9

OA: A

Is there a simple way to solve this? I solved it through quadratic equation, but lost a lot of time.

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Top Reply
Post Wed Jul 08, 2015 9:08 am
zeza wrote:
A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?

(A) 3
(B) 4
(C) 6
(D) 8
(E) 9

OA: A

Is there a simple way to solve this? I solved it through quadratic equation, but lost a lot of time.
Solution:

To solve this problem it’s easier to refer to a diagram of what is provided in the problem stem. In creating the diagram we can also fill in any variables we need to solve the problem.

ttp://postimg.org/image/4a6z1gxcj/" target="_blank">

Notice that we labeled the width of the border as x. We are given that the area of the border is 144 square inches. Knowing this, we can set up the following equation:

Area of Entire Shape - Area of Picture = Area of Border

(8 + 2x)(10 + 2x) - (8) (10) = 144

80 + 16x + 20x + 4x^2 - 80 = 144

4x^2 + 36x - 144 = 0

x^2 + 9x - 36 = 0

(x + 12)(x - 3) = 0

x = -12 or x = 3

Since we cannot have a negative length, x = 3. Thus, the width of the border is 3 inches.

Answer is A

_________________
Jeffrey Miller Head of GMAT Instruction

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Top Reply
Post Mon Dec 31, 2012 8:07 am
zeza wrote:
A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?

(A) 3
(B) 4
(C) 6
(D) 8
(E) 9

OA: A
Total area = photograph + border = (8*10) + 144 = 224.

Since the border SURROUNDS the photograph -- whose dimensions are 8 x 10 -- we get:
(border width + 8 + border width)(border width + 10 + border width) = 224.

We can plug in the answers for the width of the border.

Answer choice C: 6
(6 + 8 + 6)(6 + 10 + 6) = 20*22 = 440.
The area is almost double 224, so the width of the border must be much smaller.

Answer choice A: 3
(3 + 8 + 3)(3 + 10 + 3) = 14*16 = 224.
Success!

The correct answer is A.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

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Thanked by: Anaira Mitch
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Post Wed Jul 08, 2015 9:08 am
zeza wrote:
A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?

(A) 3
(B) 4
(C) 6
(D) 8
(E) 9

OA: A

Is there a simple way to solve this? I solved it through quadratic equation, but lost a lot of time.
Solution:

To solve this problem it’s easier to refer to a diagram of what is provided in the problem stem. In creating the diagram we can also fill in any variables we need to solve the problem.

ttp://postimg.org/image/4a6z1gxcj/" target="_blank">

Notice that we labeled the width of the border as x. We are given that the area of the border is 144 square inches. Knowing this, we can set up the following equation:

Area of Entire Shape - Area of Picture = Area of Border

(8 + 2x)(10 + 2x) - (8) (10) = 144

80 + 16x + 20x + 4x^2 - 80 = 144

4x^2 + 36x - 144 = 0

x^2 + 9x - 36 = 0

(x + 12)(x - 3) = 0

x = -12 or x = 3

Since we cannot have a negative length, x = 3. Thus, the width of the border is 3 inches.

Answer is A

_________________
Jeffrey Miller Head of GMAT Instruction

  • +1 Upvote Post
  • Quote
  • Flag
Post Mon Dec 31, 2012 8:07 am
zeza wrote:
A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?

(A) 3
(B) 4
(C) 6
(D) 8
(E) 9

OA: A
Total area = photograph + border = (8*10) + 144 = 224.

Since the border SURROUNDS the photograph -- whose dimensions are 8 x 10 -- we get:
(border width + 8 + border width)(border width + 10 + border width) = 224.

We can plug in the answers for the width of the border.

Answer choice C: 6
(6 + 8 + 6)(6 + 10 + 6) = 20*22 = 440.
The area is almost double 224, so the width of the border must be much smaller.

Answer choice A: 3
(3 + 8 + 3)(3 + 10 + 3) = 14*16 = 224.
Success!

The correct answer is A.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: Anaira Mitch
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

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