Solve.
-A picture 13 inches by 23 inches is to be mounted on a piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be if the area of the border is 252 square inches?
A)4 in
B)3 in
C)5 in
D)5.5 in

Question

Quizplus · Accepted Answer

Let x be the width of the border in inches. 
The length of the picture and matboard together will be (13+2x) inches and the width will be (23+2x) inches. 
The area of the entire piece will be (13+2x)(23+2x) square inches. 
The area of the picture itself is 13*23=299 square inches. 
Subtracting the area of the picture from the area of the entire piece gives the area of the border: 
(13+2x)(23+2x) - 299 = 252 
Simplifying the left side: 
4x^2 + 72x - 220 = 0 
Dividing each term by 4: 
x^2 + 18x - 55 = 0 
Factoring: 
(x+5)(x-11) = 0 
Since x cannot be negative, the only possible solution is x=11. 
Therefore, the width of the border will be 11/2 = 5.5 inches.

Solve. -A Picture 13 Inches by 23 Inches Is to Be