SOLUTION: A door 8 feet long and 4 feet wide is made from a pane of glass in a wooden frame b feet wide on all teh sides. The area of the entire door is 1 square foot less than three times t

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Question 447286: A door 8 feet long and 4 feet wide is made from a pane of glass in a wooden frame b feet wide on all teh sides. The area of the entire door is 1 square foot less than three times the area of wooden frame. How wide is the frame to the nearest tenth?



Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
door length = 8 ft
width == 4 ft
Glass pan length = 8-2b
glass pane width = 4-2b
Total door area - Area of pane = Area of frame
32-(8-2b)(4-2b)= arae of the frame
32= 3(32-(8-2b)(4-2b))-1
33= 3(32-(32-24b+4b^2))
/3
11=(32-(32-24b+4b^2))
11=32-32+24b^2-4b^2
4b^2-24b+11=0
Find the roots of the equation by quadratic formula
a= 4, b= -24, c= 11
Let the roots be x1.x2

b^2-4ac=576-176
b^2-4ac=400
sqrt(400)=20
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=(24+ 20)/8
x1=5.5
x2=(24-20)/8
x2=0.5
Obviously the width will be 0.5 ft.
m.ananth@hotmail.ca