ANSWER
L = 24 inches
W = 14 inches
EXPLANATION
Given tat
The length of the rectangular painting is 10 inches more than the width
Let the width of the rectangular painting be x
Recall, that the frame is 2 inches thick. This implies that there re 2 inches to the left ogf the length and 2 inches to the right of the length. So, there are more 4 inches to the length of the picture
Hence, the new length is
L = (x + 10) + 4
L = x + 10 + 4
L = x + 14
Also, for the width of the painting, we have
w = x + 4
Recall, that the area of a rectangle is given below as
Area = L x W
[tex]\begin{gathered} \text{ Area of a rectangle = L x W} \\ \text{ L = x + 14, and W = x + 4, and A = 336 in}^2 \\ \text{ 336 = \lparen x }+\text{ 14\rparen \lparen x }+\text{ 4\rparen} \\ \text{ Open the parentheses} \\ \text{ 336 = x}^2\text{ + 4x + 14x + 56} \\ \text{ 336 = x}^2\text{ + 18x + 56} \\ \text{ x}^2\text{ + 18x + 56 = 336} \\ \text{ x}^2\text{ + 18x + 56 - 336 =0} \\ \text{ x}^2\text{ + 18x - 280 = 0} \end{gathered}[/tex]Find the value of x by using factorizatin method
[tex]\begin{gathered} \text{ x}^2\text{ }+\text{ 28x - 10x - 280 = 0} \\ \text{ x\lparen x + 28\rparen - 10\lparen x + 28\rparen = 0} \\ \text{ \lparen x - 10\rparen \lparen x + 28 \rparen = 0} \\ \text{ \lparen x - 10\rparen = 0 or \lparen x + 28\rparen = 0} \\ \text{ x = 0 + 10 or x = 0 - 28} \\ \text{ x = 10 or x = -28} \end{gathered}[/tex]Find the length and the width of the rectngular painting
L = x + 14
L = 10 + 14
L = 24 inches
width
W = x + 4
W = 10 + 4
W = 14 inches