Answer:
Length = 24 and Width = 81
Step-by-step explanation:
Let Width be W
then Length = W-57
Perimeter of rectangle = 2(Length + Width)
=2 (W-57+W)= 210
4W- 114= 210
4W= 324
W= 81
Then Length = 81-57 = 24
The length and width of a regulation singles tennis court is 78 feet and 27 feet respectively when the perimeter is 210 feet and length is 57 feet less than five times the width. This can be obtained by using formula of perimeter of a rectangle and algebraic expression.
P = 2(l + b) where P is the perimeter of the rectangle, l is the length of the rectangle and b is the width of the rectangle.
Length of the rectangle is 57 feet less than five times the width, that is, in the form of algebraic expression,
l = 5b - 57 , where l and b are length and width.
Given that, perimeter P=210 feet, length l= 5b - 57, width b = b
P = 2(l + b)
210 = 2((5b - 57) + b)
210 = 2(5b + b -57) =2(6b - 57)
210 = 12b - 114
12b = 210 + 114 = 324
b = 324/12 =27 ⇒b = 27 feet
l = 5b - 57
l = 5(27) - 57
l =135 - 57 =78 ⇒ l = 78 feet
l = 78 feet and b = 27 feet
Hence the length and width of a regulation singles tennis court is 78 feet and 27 feet respectively when the perimeter is 210 feet and length is 57 feet less than five times the width.
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