1. ## 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?

2. Hello, magentarita!

Did you make a sketch?

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.

3. ## amazing.........

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.