# 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?

##### 1 Answer

Width:

Length:

#### 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

#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 * (l + w) = 176#

Use the value of

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

#2w + 8 + 2w = 176#

#4w = 168 implies w = 168/4 = color(green)(42)#

Use this value to find

#l = w + 4 = 42 + 4 = color(green)(46)#

The dimensions of the painting are