SOLUTION: This is from Activity Bank, INTEGRATED MATHEMATICS 1 Copyright by Houghton Mifflin Company. One of the world's largest paintings is "The Battle of Gettysburg." When it was compl

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: This is from Activity Bank, INTEGRATED MATHEMATICS 1 Copyright by Houghton Mifflin Company. One of the world's largest paintings is "The Battle of Gettysburg." When it was compl      Log On

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Question 196134: This is from Activity Bank, INTEGRATED MATHEMATICS 1 Copyright by Houghton Mifflin Company.
One of the world's largest paintings is "The Battle of Gettysburg." When it was completed in 1883 by a French artist and 16 assistants, it covered an area of 28,700 ft. The perimeter was 960 ft. Find thd length and width of the painting.
Answer by Earlsdon(6287) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the formula for the area of a rectangle:
A+=+L%2AW and this is equal to 28,700 sq.ft.
Now do the formula for the perimeter of a rectangle:
P+=+2%28L%2BW%29 and this is equal to 960 ft.
Rewrite the perimeter as:
2%28L%2BW%29+=+960 Divide both sides by 2.
L%2BW+=+480 Rearrange:
L+=+480-W Substitute this for L in the area equation below:
L%2AW+=+28700
%28480-W%29%2AW+=+28700 Simplify.
480W-W%5E2+=+28700 Rearrange:
W%5E2-480W%2B28700 Factor:
%28W-410%29%28W-70%29+=+0 Apply the zero product rule.
W-410+=+0 or W-70+=+0 so...
W+=+410 or W+=+70 Choose the smaller value for the width, W:
W+=+70 and...
L+=+480-W
L+=+480-70
L+=+410
The length of the painting is 410 ft.
The width of the painting is 70 ft.