# Algebra

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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.

• Algebra -

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

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L ^ 2 - 55 L + 650 = 0

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• Algebra -

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L ^ 2 - 55 L + 650 = 0

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When page be open in blue rectangle type:

x ^ 2 - 55 x + 650 = 0

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• Algebra -

CORRECTION :

When page be open in blue rectangle type:

x ^ 2 - 55 x + 650

Set:

Range x-axis from - 20 to 80

Range y-axis from - 200 to 800

And click option: Draw