SOLUTION: a frame painting has overall dimensions of 32 inches by 29 . the area of the painting itself is 378 squares inches. find the width if the frame

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Question 1002544: a frame painting has overall dimensions of 32 inches by 29 . the area of the painting itself is 378 squares inches. find the width if the frame
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Basically this will use Overall-Painting=Frame.

Setup some variables and try to do any computations later instead of sooner.
system%28w=29%2CL=32%2CA=378%2Cu=unknownFrameWidth%29
A is for area of the painting, NOT including frame.

Overall Area, wL
Painting's Area, (w-2u)(L-2u)
Frame Area, assigned to variable A
-
Referring to the basic idea at the top,
highlight_green%28wL-%28w-2u%29%28L-2u%29=A%29

Begin simplifying that equation.
wL-%28wL-2Lu-2wu%2B4u%5E2%29-A=0
wL-wL%2B2Lu%2B2wu-4u%5E2-A=0
2Lu%2B2wu-4u%5E2-A=0
-4u%5E2%2B2Lu%2B2wu-A=0
4u%5E2-2Lu-2wu%2BA=0
Finish simplying
highlight%284u%5E2-%282L%2B2w%29u%2BA=0%29

Solve for u. You can substitute the given values whenever you feel the need. Your choice either to solve for u completely in symbols, or substitute the given values now and finish that way.