Answer:
Length = 82.5 feet
Width = 17.5 feet
Explanation:
The formula for the Perimeter of a rectangle = 2(Length + Width)
= 2L + 2W
We are told in the question that: Darrin is hanging 200 feet of Christmas garland on the fencing that encloses his rectangular front yard
Hence, The perimeter of the rectangular front yard = 200 feet
200 = 2( L + W).........Equation 1
Also, the length is 5 feet less than 5 times the width
L = 5W - 5
Hence,
200= 2(5W - 5 + W)
200 = 2(5W + W - 5)
200 = 2(6W - 5)
200 = 12W - 10
Collect the like terms
200 + 10 = 12W
210 = 12W
W = 210/12
W = 17.5 feet
Substitute 17.5 for W in Equation 1
200 = 2( L + W).........Equation 1
200 = 2( L + 17.5)
200 = 2L + 35
200 - 35 = 2L
2L = 165
L = 165/2
L = 82.5 feet
Therefore, the Length of the rectangular fence = 82.5 feet while the Width of the rectangular fence is 17.5 feet.