SOLUTION: A 4 by 6 inch photograph is to be matted such that the area of the mat is double the area of the photo. Assuming that the mat is the same width all around the picture,what is the

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A 4 by 6 inch photograph is to be matted such that the area of the mat is double the area of the photo. Assuming that the mat is the same width all around the picture,what is the       Log On


   

Question 118650: A 4 by 6 inch photograph is to be matted such that the area of the mat is double the area of the photo. Assuming that the mat is the same width all around the picture,what is the width of the mat ?
I tried (4-2x)(6-2x) and ended up with (x+4)(x-3)=0 and said witdth of mat was 3 inches but lost marks :( Can anyone explain this problem to me ?
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
4*6=24 square inches is the area of the picture.
Thus the mat area must be 4*24=96 square inches.
The measurements of the mat is (4+2X)(6+2X).
The addition of the 2x to the picture measurements is because the mat is equal for the width & the length of the picture.
Now you have:
(4+2x)(6+2x)=96
24+12x+8x+4x^2=96
4x^2+20x+24-96=0
4x^2+20x-72=0
4(x^2+5x-18)=0
Using the quadratic equation: x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ we get:
x=(-5+-sqrt[5^2-4*1*-18])/2*1
x=(-5+-sqrt[25+72])/2
x=(-5+-sqrt97)/2
x=(-5+-9.85)/2
x=(-5+9.85)/2
x=4.85/2
x=2.425 inches is the answer for the width of the mat.
Proof
(4+2*2.425)(6+2*2.425)=96
(4+4.85)(6+4.85)=96
8.85*10.85=96
96=96