Algebra
posted by Bernadette on .
How to find dimensions of a field when given length of fencing and area?
Hi I really appreciate your help on this.
The question states that I have a field of area 650 square metres and fencing of 110 metres. I must give 3 possible sets of dimensions of the field and the fencing need not cover all four sides of the field.
Oh I forgot to mention that quadratic algebra and graphing utility must be used.
Thank you so much.

A = Area
F = Fencing
W = Width
L = Length
A = W * L = 650 m ^ 2
W * L = 650 Divide both sides by L
W = 650 / L
F = 2 W + 2 L = 2 ( W + L ) = 110 m
2 ( W + L ) = 110 Divide both sides by 2
W + L = 110 / 2
W + L = 55
650 / L + L = 55 Multiply both sides by L
650 + L * L = 55 L
650 + L ^ 2 = 55 L
L ^ 2  55 L + 650 = 0
The exact solutions are :
L = ( 5 / 2 ) * [ 11 + sqrt ( 17 ) ]
approx. 37.81 m
and
L = (  5 / 2 ) * [  11 + sqrt ( 17 ) ]
approx. 17.19 m
When L = 37.81 m
W = 650 / 37.81 = 17.19 m
When L = 17.19 m
W = 650 / 17.19 = 37.81 m
Dimensions of a field:
37.81 m X 17.19 m
If you don't know how solve equation L ^ 2  55 L + 650 = 0
in google type:
quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type:
L ^ 2  55 L + 650 = 0
and click option: solve it!
You wil see solution stepbystep 
If you must draw function :
L ^ 2  55 L + 650 = 0
In google type:
functions graphs online
When you see list of results click on:
rechneronline.de/functiongraphs/
When page be open in blue rectangle type:
x ^ 2  55 x + 650 = 0
Set:
Range xaxis from  20 to 80
Range yaxis from  200 to 800
And click option: Draw 
CORRECTION :
When page be open in blue rectangle type:
x ^ 2  55 x + 650
Set:
Range xaxis from  20 to 80
Range yaxis from  200 to 800
And click option: Draw