SOLUTION: The frame around the picture in the illustration has a constant width. how wide is the frame if the area equals the area of the picture
the illustration is
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the illustration is
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Question 214239This question is from textbook
: The frame around the picture in the illustration has a constant width. how wide is the frame if the area equals the area of the picture
the illustration is a square inside a squre. the frame
with a width of 12 inches and a hight of 10 inches
I hope thats enough info 2 help me
You can put this solution on YOUR website! The frame around the picture in the illustration has a constant width. how wide is the frame if the area equals the area of the picture
the illustration is a square inside a squre. the frame
with a width of 12 inches and a hight of 10 inches
.
Draw a diagram of the problem, label all the information given it'll help you see the solution.
.
Let w = width of frame
then measure of picture is:
12-2w = width of picture
10-2w = length of picture
.
Area of picture is (length times width):
(12-2w)(10-2w)
.
Area of frame:
2(10w) + 2w(12-2w)
.
Setting them equal":
(12-2w)(10-2w) = 2(10w) + 2w(12-2w)
120-24w-20w+4w^2 = 20w + 24w - 4w^2
120-44w+4w^2 = 44w - 4w^2
8w^2+120-44w = 44w
8w^2-88w+120 = 0
w^2-11w+15 = 0
Using the quadratic equation we get two solutions:
w={9.40512483795333, 1.59487516204667}
It wouldn't make sense to have a 9+ inch width frame so the answer MUST be:
w = 1.595 inches (width of frame)
.
Details of the quadratic equation to follow:
