A border of uniform width is placed

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?

3 Explanations

▲

sourabh parulekar

This can also be solved as follows:

Area of photo = 8*10 = 80 sq. in.
Area of border = 144 sq. in (given)
New area of photo along with the border = 80+144 = 224 sq. in.

Now we can find new lengths in equal integer increments of 8 and 10 (since answer choices are integers)

+6 works as (8+6)*(10+6) = 16*14 =224

Last step, since border is of equal width on either side of the length and width of the photo, then the width of the border is 6/2 = 3.

No quadratics req. Is this approach correct?

Oct 12, 2015 • Comment

Cydney Seigerman, Magoosh Tutor

Hi Sourabh,

Yes, this is a perfectly good approach to solve this problem :)

We can describe of the total area (photo+border) as the product of the total length and total width:

(8+2w)*(10+2w)

where w is the width of the border. I've written 2w since, as you astutely mentioned, the border on both sides of the width and length must be accounted for. As you mentioned, this area will be equal to the sum of the area of the photo and border.

Great job :D

Oct 25, 2015 • Reply

▲

Joseph Lucaj

Why are the 4 side lengths of the border 10x and 8x?

Jun 22, 2015 • Comment

Jonathan , Magoosh Tutor

Those are not the side lengths; those are the rectangle areas.

We are dividing the border into 8 pieces: 4 squares at the corners with side x and 4 rectangles at the sides. 2 of the rectangles have are x by 10, and the other 2 are x by 8. So their respective areas are 10 * x = 10x and 8 * x = 8x. So the total area of the border is:

4 * x(x) + 2(10x) + 2(8x) =

4x^2 + 36x

Hope that helps.

Jun 29, 2015 • Reply

▲

Mike McGarry, Magoosh Tutor