SOLUTION: The area of a rectangular plot 24 feet long and 16 feet wide will be doubled by adding an equal distance to each side of the plot. What is the distance added to each side?

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Question 623696: The area of a rectangular plot 24 feet long and 16 feet wide will be doubled by adding an equal distance to each side of the plot. What is the distance added to each side?
Found 2 solutions by ewatrrr, MathTherapy:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,  

The area of a rectangular plot 24 feet long and 16 feet wide will be doubled 

by adding an equal distancehighlight%28x%29to each side of the plot.

Question states*** Note: A = l*w

 2(24*16) = (24 + 2x)16

   48 -24 = 2x

    x = 12' the distance added to each side

and

CHECKING our Answer***

  48%2A16+=+768+=++2%2A24%2A16+=+2%2A384

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

The area of a rectangular plot 24 feet long and 16 feet wide will be doubled by adding an equal distance to each side of the plot. What is the distance added to each side?

Area = 24 * 16, or 384 sq ft
Doubling this area makes it 384 * 2, or 768 sq ft

Let distance added to each side of rectangle be D
Then: (24 + D)(16 + D) = 768

384+%2B+40D+%2B+D%5E2+=+768

D%5E2+%2B+40D+-+384+=+0

(D + 48)(D - 8) = 0

D, or distance added to each side = - 48 (ignore), or highlight_green%288%29 ft

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Check
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(24 + 8) * (16 + 8) = 768

32 * 24 = 768

768 = 768 (TRUE)

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