SOLUTION: A Painting canvas has a length 8 inches longer than its width. if the area is 84in^2 what are the dimensions of the canvas

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Question 149494: A Painting canvas has a length 8 inches longer than its width. if the area is 84in^2 what are the dimensions of the canvas
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

The area of any rectangle is A=W%2AL. Since the "length 8 inches longer than its width", this tells us that L=W%2B8


A=W%2AL Start with the given area equation.


84=W%28W%2B8%29 Plug in A=84 (the given area) and L=W%2B8


84=W%5E2%2B8W Distribute

0=W%5E2%2B8W-84 Subtract 84 from both sides.


Let's use the quadratic formula to solve for W


W+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


W+=+%28-%288%29+%2B-+sqrt%28+%288%29%5E2-4%281%29%28-84%29+%29%29%2F%282%281%29%29 Plug in a=1, b=8, and c=-84


W=+%28-8+%2B-+sqrt%28+64-4%281%29%28-84%29+%29%29%2F%282%281%29%29 Square 8 to get 64.


W+=+%28-8+%2B-+sqrt%28+64--336+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-84%29 to get -336


W+=+%28-8+%2B-+sqrt%28+64%2B336+%29%29%2F%282%281%29%29 Rewrite sqrt%2864--336%29 as sqrt%2864%2B336%29


W+=+%28-8+%2B-+sqrt%28+400+%29%29%2F%282%281%29%29 Add 64 to 336 to get 400


w+=+%28-8+%2B-+sqrt%28+400+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


W+=+%28-8+%2B-+20%29%2F%282%29 Take the square root of 400 to get 20.


W+=+%28-8+%2B+20%29%2F%282%29 or W+=+%28-8+-+20%29%2F%282%29 Break up the expression.


W+=+%2812%29%2F%282%29 or W+=++%28-28%29%2F%282%29 Combine like terms.


W+=+6 or W+=+-14 Simplify.


Since a negative width is not possible, this means that the only solution is W+=+6

So the width is 6 inches

L=W%2B8 Go back to the second equation.


L=6%2B8 Plug in W+=+6


L=14 Add

So the length is 14 inches



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Answer:


So the canvas is 6 in by 14 in