# Photo Dimensions

• Nov 25th 2008, 10:18 PM
magentarita
Photo Dimensions
A photo is 3 inches longer that it is wide. A 2-inch border is placed around the photo making the total area of the photo and border 108 square inches. What are the dimensions of the photo?
• Nov 26th 2008, 04:43 AM
Soroban
Hello, magentarita!

Did you make a sketch?

Quote:

A photo is 3 inches longer that it is wide.
A 2-inch border is placed around the photo.
The total area of the photo and border is 108 square inches.
What are the dimensions of the photo?

Code:

        : 2 :  - W+3 -  : 2 :       - *---*-----------*---*  -       2 |  :          :  |  :       - * - *-----------* - *  :       : |  |          |  |  :       W |  |W          |  | W+4       : |  |    W+3    |  |  :       - * - *-----------* - *  :       2 |  :          :  |  :       - *---*-----------*---*  -         : - - -  W+7  - - - :

Let $\displaystyle W$ = width of the photo.
Then $\displaystyle W + 3$ = length of the photo.

With a two-inch border, the object has length $\displaystyle W + 7$ and width $\displaystyle W+4$

The total area is 108: .$\displaystyle (W+7)(W+4) \:=\:108 \quad\Rightarrow\quad W^2 + 11W - 80 \:=\:0$

. . which factors: .$\displaystyle (W - 5)(W + 16) \:=\:0$

. . and has the positive root: .$\displaystyle W \,=\,5$

Therefore, the dimensons of the photo are: .$\displaystyle 5 \times 8$ inches.

• Nov 28th 2008, 05:07 AM
magentarita
amazing.........
Quote:

Originally Posted by Soroban
Hello, magentarita!

Did you make a sketch?

Code:

        : 2 :  - W+3 -  : 2 :       - *---*-----------*---*  -       2 |  :          :  |  :       - * - *-----------* - *  :       : |  |          |  |  :       W |  |W          |  | W+4       : |  |    W+3    |  |  :       - * - *-----------* - *  :       2 |  :          :  |  :       - *---*-----------*---*  -         : - - -  W+7  - - - :
Let $\displaystyle W$ = width of the photo.
Then $\displaystyle W + 3$ = length of the photo.

With a two-inch border, the object has length $\displaystyle W + 7$ and width $\displaystyle W+4$

The total area is 108: .$\displaystyle (W+7)(W+4) \:=\:108 \quad\Rightarrow\quad W^2 + 11W - 80 \:=\:0$

. . which factors: .$\displaystyle (W - 5)(W + 16) \:=\:0$

. . and has the positive root: .$\displaystyle W \,=\,5$

Therefore, the dimensons of the photo are: .$\displaystyle 5 \times 8$ inches.

Soroban, you are amazing in terms of math. Through your help, I will be ready for calculus next semester. Are you willing to help me? I have to take calculus 1-3, differential equations and linear algebra in future semesters.

Thanks again.