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Jackie and Ken are building a fence around a rectangular field.  They want to enclose an area of 75 square feet.  The width should be 3 feet longer than the length of the field.  What are the dimensions of the field?  Round to the nearest tenth, if necessary.

Whiz333  Apr 15, 2017
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Let the length =L

Then the width =L+3

 

L x {L+3} =75

Solve for L:
L (L + 3) = 75

Expand out terms of the left hand side:
L^2 + 3 L = 75

Add 9/4 to both sides:
L^2 + 3 L + 9/4 = 309/4

Write the left hand side as a square:
(L + 3/2)^2 = 309/4

Take the square root of both sides:
L + 3/2 = sqrt(309)/2 or L + 3/2 = -sqrt(309)/2

Subtract 3/2 from both sides:
L = sqrt(309)/2 - 3/2 or L + 3/2 = -sqrt(309)/2

Subtract 3/2 from both sides:
Answer: | L = sqrt(309)/2 - 3/2 =~7.3 feet - the length of the field

The width =7.3 + 3 =10.3 feet

Guest Apr 15, 2017

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