SOLUTION: A rectangular canvas picture measures 22 inches by 24 inches. The canvas is mounted inside a frame of uniform width, increasing the total area covered by both canvas and frame to

Algebra ->  Surface-area -> SOLUTION: A rectangular canvas picture measures 22 inches by 24 inches. The canvas is mounted inside a frame of uniform width, increasing the total area covered by both canvas and frame to      Log On


   

Question 964996: A rectangular canvas picture measures 22 inches by 24 inches. The
canvas is mounted inside a frame of uniform width, increasing the total
area covered by both canvas and frame to 728 square inches. Find the
uniform width of the frame.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You could assign variables to everything.
u, one dimension of the canvas
v, other dimension of the canvas
A, total area of frame plus canvas
w, the uniform width of the border

You should draw a picture and label everything because this usually helps.

highlight_green%28A=%28u%2B2w%29%28v%2B2w%29%29, main equation purely in symbolic form. The unknown variable is w.

uv%2B2vw%2B2uw%2B4w%5E2=A
4w%5E2%2B%282v%2B2u%29w%2Buv-A=0
4w%5E2%2B%282u%2B2v%29w%2Buv-A=0
highlight_green%284w%5E2%2B%282u%2B2v%29w%2B%28uv-A%29=0%29.

You could continue in symbolic form to solve for w using general solution formula for a quadratic equation, but maybe more comfortable to substitute the given values NOW, and then use the general formula solution.
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u=22
v=24
A=728