+101 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.
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
