SOLUTION: A rectangular picture 24 inches by 32 inches is surrounded by a border of uniform width. If the area of the border is 528 square inches less than the area of the picture, find the

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Question 565119: A rectangular picture 24 inches by 32 inches is surrounded by a border of uniform width. If the area of the border is 528 square inches less than the area of the picture, find the width of the border?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Length of picture = 32
Width = 24

Area = 768 In^2
Let the width of frame be x
..
Area = 768 In^2
Area of framework = 240 In^2
Length of picture+width =32+2x
width of picture+width= 24+2x

(32+2x )(24+2x)-240= 768

768+64x +48x+4x^2-240= 768
4X^2+112x-240= 0
Find the roots of the equation by quadratic formula
a= 4 b= 112 c= -240
b^2-4ac= 12544 + 3840
b^2-4ac= 16384
sqrt%28%0916384%09%29= 128
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=( -112 + 128 )/ 8
x1= 2
x2=( -112 -128 ) / 8
x2= -30
Ignore negative value
width = 2 inches