SOLUTION: Hi, I'm having trouble solving and figuring out what to do with this problem: A rectangular picture 16 inches by 20 inches has a frame of uniform width. Find the width of the fr

Algebra ->  Equations -> SOLUTION: Hi, I'm having trouble solving and figuring out what to do with this problem: A rectangular picture 16 inches by 20 inches has a frame of uniform width. Find the width of the fr      Log On


   

Question 1027171: Hi, I'm having trouble solving and figuring out what to do with this problem:
A rectangular picture 16 inches by 20 inches has a frame of uniform width. Find the width of the frame if the total area of the picture and the frame is 672 square inches.
Thank you.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Length of photo = 20 in
Width = 16 in
Total area = 672
Area of picture DISABLED_event_only= 320 m^2
Area of border = 352 m^2
Length of picture+border= 20 + 2 x
width of picture+border = 16 + 2 x

( 20 + 2 x ) ( 16 + 2 x ) + -320 = 352

320 + 40 x + 32 x + 4 X^2 + -320 = 352
4 X^2 + 72 x + -352 = 0
Find the roots of the equation by quadratic formula
a= 4 b= 72 c= -352
b^2-4ac= 5184 - -5632
b^2-4ac= 10816 sqrt%28%0910816%09%29= 104
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( -72 + 104 )/ 8
x1= 4
x2=( -72 -104 ) / 8
x2= -15.5
Ignore negative value
width of border 4 in