Question

The area of a rectangular tennis court is 140 square meters. It's length is 6 meters less than twice it's width. Find the dimensions of the tennis court

Answer 1

Answer: length = 14 meters

Width = 10 meters

Step-by-step explanation:

The rectangular tennis court has two equal lengths,L and two equal widths,W

The area of the tennis court is expressed as

Area = Length × width

The area is given as 140 square meters. It means that

L× W = 140

It's length is 6 meters less than twice it's width. It means that

L = 2W - 6

Substituting L = 2W - 6 into LW = 140, it becomes

W(2W - 6) = 140

2W^2 - 6W = 140

2W^2 - 6W - 140 = 0

W^2 - 3W - 70 = 0

W^2 + 7W - 10W - 70 = 0

W( W + 7 ) - 10( W + 7) = 0

( W + 7 )(W - 10) = 0

( W + 7 ) = 0 or W - 10 = 0

W= -7 or W = 10 meters

The value cannot be negative so W = 10

L = 2W - 6 = 2×10 - 6

L = 20 - 6 = 14 meters