Photo Dimensions

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November 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?
November 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 $W$ = width of the photo.
Then $W + 3$ = length of the photo.

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

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

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

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

Therefore, the dimensons of the photo are: . $5 \times 8$ inches.
November 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 $W$ = width of the photo.
Then $W + 3$ = length of the photo.

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

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

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

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

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