+136 Sarah is trying to fence a rectangular area containing at least 100 sq. ft while using the least amount of material to build the fence. The length of the rectangular area should be 15 ft longer than the width. What should the width, in ft, be?
Let the Width=W
The Length=W+15
W x [W+15]=100
Solve for W:
W (W+15) = 100
Expand out terms of the left hand side:
W^2+15 W = 100
Add 225/4 to both sides:
W^2+15 W+225/4 = 625/4
Write the left hand side as a square:
(W+15/2)^2 = 625/4
Take the square root of both sides:
W+15/2 = 25/2 or W+15/2 = -25/2
Subtract 15/2 from both sides:
W = 5 or W+15/2 = -25/2
Subtract 15/2 from both sides:
Answer: | W = 5 or W = -20 , So the Width=5 feet The Length=5+15 =20 feet
