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

Sep 23, 2015

I found $4.5 \text{yd" and 26.5"yd}$

#### Explanation:

I supposed that you had a rectangular garden:

So:
$62 = 2 x + 2 y$
$120 = x y$

From the second: $x = \frac{120}{y}$ substituted into the first:
$62 = 2 \cdot \frac{120}{y} + 2 y$ rearranging:
$2 {y}^{2} - 62 y + 240 = 0$
${y}_{1 , 2} = \frac{62 \pm \sqrt{3844 - 1920}}{4} = \frac{62 \pm \sqrt{1924}}{4}$
${y}_{1} = 4.534$
${y}_{2} = 26.466$
We can choose the first, $y = 4.534 \approx 4.5$, to get $x = 26.466 \approx 26.5$ (or viceversa).