SOLUTION: A photograph is 12 cm longer than it is wide. It is mounted in a frame 5 cm wide. The area of the frame is 620 cm squared. What is the dimensions of the photo

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Question 965121: A photograph is 12 cm longer than it is wide. It is mounted in a frame 5 cm wide. The area of the frame is 620 cm squared. What is the dimensions of the photo

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x and y, photograph dimensions.
a, the area of just the frame, alone

y=12%2Bx, assuming y is length.
Let u be the uniform width of the frame.

Total area frame plus photograph,%28x%2B2u%29%28y%2B2u%29
area of just the photograph,xy
area of just the frame,%28x%2B2u%29%28y%2B2u%29-xy

According to description and assigning,
%28x%2B2u%29%28y%2B2u%29-xy=a
xy%2B2yu%2B2xu%2B4u%5E2-xy-a=0
2yu%2B2xu%2B4x%5E2-a=0
and through substituting according to description,
2%2812%2Bx%29u%2B2xu%2B4x%5E2-a=0
24u%2B2ux%2B2ux%2B4x%5E2-a=0
4x%5E2%2B4ux%2B24u-a=0
highlight_green%284x%5E2%2B4ux%2B%2824u-a%29=0%29

Now would be a good step to substitute the given values, compute constant and coefficients and then finish solving for x.
Use as described:
x, unknown photograph width
u=5
a=620
y=12+x