SOLUTION: the length of a badminton court is 4m more than twice its width. if the area of the court is 79.2 m, find its dimensions to the nearest meter. *step by step working thank for

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Question 528008: the length of a badminton court is 4m more than twice its width. if the area of the court is 79.2 m, find its dimensions to the nearest meter.
*step by step working
thank for your cooperation
Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
Area of the Court = A = 79.2 square meter
Length = L = W +4 m
Width = ?
Length = ?
Area of rectangle = Length * Width
A=L*W
79.2 = (W+4)W
79.2=w^2+4W
w^2+4W-79.2=0
Solve for 'w'
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aw%5E2%2Bbw%2Bc=0 (in our case 1w%5E2%2B4w%2B-79.2+=+0) has the following solutons:

w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A1%2A-79.2=332.8.

Discriminant d=332.8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+332.8+%29%29%2F2%5Ca.

w%5B1%5D+=+%28-%284%29%2Bsqrt%28+332.8+%29%29%2F2%5C1+=+7.1214034007931
w%5B2%5D+=+%28-%284%29-sqrt%28+332.8+%29%29%2F2%5C1+=+-11.1214034007931

Quadratic expression 1w%5E2%2B4w%2B-79.2 can be factored:
1w%5E2%2B4w%2B-79.2+=+1%28w-7.1214034007931%29%2A%28w--11.1214034007931%29
Again, the answer is: 7.1214034007931, -11.1214034007931. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-79.2+%29


w=7.121 or w=-11.121 (inadmissible)
So w = 7.12
Length = L = W +4 = 7.12+4
Length = L = W +4 = 11.12 meter

Dimension of the Court
=====================
Length = 11.12meter
Width = 7.12meter
Area = 79.2 square meter