SOLUTION: it's a word problem. Nancy wants to buy a mat for a photographtaht measures 14 in by 20 in. She wants to have an even border around the picture when it is mounted on the mat.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: it's a word problem. Nancy wants to buy a mat for a photographtaht measures 14 in by 20 in. She wants to have an even border around the picture when it is mounted on the mat.       Log On


   

Question 112928: it's a word problem.
Nancy wants to buy a mat for a photographtaht measures 14 in by 20 in. She wants to have an even border around the picture when it is mounted on the mat. If the area of the mat is 352 in squared How wide will the border be? I know the anwser is 1 inch. I just don't see why.

Here's what I've tried.
A=LW
(14+x)squared (20+x)Squared
280+14x + 20x+xSquared
280+34x+xsquared=0
Since this can't be factored i subtracted the 280 from both sides and got
x2 +34x = -280
half of 34 is 17 and 17 times 17 is 136
So this becomes
x2 +34x + 136 = -144
(x-72)squared = -144
x-72 = sqare root of -144
x-72 = 12i
x=72+or-12i
but this doesn't equal 1 inch. Please help me
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let x="width of border"

if the photo is 14 by 20, then the mat will be (14+2x) by (20+2x)
___ an x width border on both ends of length and width

so the area is (14+2x)(20+2x), which equals 352

280+68x+4x^2=352 ___ x^2+17x-18=0 ___ (x+18)(x-1)=0