The Browns installed 58 feet of fencing around a rectangular play yard. If the yard covers 204 square feet, what are its dimensions?

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01-12-2016
Mathematics

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The Browns installed 58 feet of fencing around a rectangular play yard. If the yard covers 204 square feet, what are its dimensions?

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wizard123 wizard123 · Answer 1 · 2016-12-01T11:52:39+01:00

wizard123 wizard123

01-12-2016

P = 2L +2w = 58 ----> L+w = 29 ----> L = 29-w

A = L*w = 204

Now substitute "29-w" for L in Area equation:

(29-w)w = 204

This gives a quadratic

w^2 - 29w + 204 = 0

Use quadratic formula:

[tex]w = \frac{29 \pm \sqrt{29^2 -4(1)(204)}}{2} = \frac{29 \pm 5}{2}[/tex]

w = 12, w = 17

Either value will work since L=29-w, the other number becomes length.

Therefore the final dimensions of the rectangle are 12 by 17.

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