Border of photograph

I did this in this way and it was little bit quicker -

Let x be the border width
Given -- (8+2x) x (10+2x) - 80 = 144

Factoring 4 out from the LHS, and then diving it by RHS

(x+4)*(x+5)=56

Now, look the options, a quick look tells us that 56 = 7*8 and if we put x = 3 we will get the required number

Thus, correct answer is (a)
Hope this helps!

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.

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.



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