The perimeter of a garden is 62 yd and the area is 120yd^2, how do you find the dimensions?

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The perimeter of a garden is 62 yd and the area is 120yd^2, how do you find the dimensions?

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Answer 1 · 2015-09-23T00:34:05

I found $4.5 yd and 26.5 yd$ $4.5"yd" and 26.5"yd"$

Explanation:

I supposed that you had a rectangular garden:
enter image source here
So:
$62 = 2 x + 2 y$ $62=2x+2y$
$120 = x y$ $120=xy$

From the second: $x = \frac{120}{y}$ $x=120/y$ substituted into the first:
$62 = 2 \cdot \frac{120}{y} + 2 y$ $62=2*120/y+2y$ rearranging:
$2 y^{2} - 62 y + 240 = 0$ $2y^2-62y+240=0$
Using the Quadratic Formula:
$y_{1, 2} = \frac{62 \pm \sqrt{3844 - 1920}}{4} = \frac{62 \pm \sqrt{1924}}{4}$ $y_(1,2)=(62+-sqrt(3844-1920))/4=(62+-sqrt(1924))/4$
You get two solutions:
$y_{1} = 4.534$ $y_1=4.534$
$y_{2} = 26.466$ $y_2=26.466$
We can choose the first, $y = 4.534 \approx 4.5$ $y=4.534~~4.5$ , to get $x = 26.466 \approx 26.5$ $x=26.466~~26.5$ (or viceversa).

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The perimeter of a garden is 62 yd and the area is 120yd^2, how do you find the dimensions?

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Explanation:

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