# Julia framed an oil painting that her uncle gave her. The painting was 4 inches longer than it was wide and took 176 inches of frame molding, what were the dimensions of the picture?

Sep 10, 2015

Width: $\text{42 in}$
Length: $\text{46 in}$

#### Explanation:

The information given to you will allow you to write two equations with two unknowns, the width and the length of the painting.

First of all, you know that the painting's length is 4 inches longer than its width. If you take the width to be $w$ and the length to be $l$, you can write

$l = w + 4$

Secondly, you know that it took a total of 176 inches of molding to completely frame the painting. Since the painting is a rectangle, you know that the amount of frame molding used must have accounted for two widths and two lengths.

In other words, the perimeter of the rectangle is equal to 176 inches

$P = 2 \cdot \left(l + w\right) = 176$

Use the value of $l$ from the first equation to find out the width of the painting

$2 l + 2 w = 176$

2 * (w + 4) + 2w = 176#

$2 w + 8 + 2 w = 176$

$4 w = 168 \implies w = \frac{168}{4} = \textcolor{g r e e n}{42}$

Use this value to find $l$

$l = w + 4 = 42 + 4 = \textcolor{g r e e n}{46}$

The dimensions of the painting are $\text{42 in" xx "46 in}$.