SOLUTION: Please help. A picture 19 inches by 24 inches is to be mounted on as piece of matboard so that there is an even amount of mat all around the picture. How wide will the border be

Question 314425: Please help. A picture 19 inches by 24 inches is to be mounted on as 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 188 sq. in? Please show all work necessary to arrive to the solution.
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
19*24=456 IN^2 IS THE AREA OF THE PICTURE.
(19+2X)(24+2X)=456+188
456+48X+38X+4X^2=644
4X^2+86X+456-644=0
4X^2+86X-188=0
(2X-4)(2X+47)=0
2X-4=0
2X=4
X=4/2
X=2 ANS. FOR THE BORDER WIDTH.
PROOF:
(19+2*2)(24+2*2)=456+188
(19+4)(24+4)=644
23*28=644
644=644
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