Question by vluenvy: 8×10 photograph and frame. Find x.?
Suppose that we have an 8×10 cm photograph which is surrounded by a frame of uniform width x. If the area of the frame is equal to the area of the photograph, what is X?
i tried it like 20 times, each time the answer doesnt fit. help please.
Answer by bpascal
First, the area of the photograph is 80 cm^2, so this must be the area of the frame as well.
Second, draw a diagram of the photograph surrounded by the uniform thickness frame and label the thickness x.
If we look at the diagrams dimensions including the frame we have
(8 + 2x) X (10 + 2x) and this total area must equal 2 times 80, since we have the photograph and frame area together. So,
(8 + 2x)(10 + 2x) = 160
4x^2 + 36x + 80 = 160
4x^2 + 36x – 80 = 0
x^2 + 9x – 20 = 0
x = [-9 +- sqrt(161)] / 2
The solution with the negative sqrt will be extraneous since x must be positive.
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