Question

mp modeling real life a farmer plants beets in a square garden with side lengths of $12\frac{2}{3}$ feet. he plants squash in a garden with a perimeter of $50\frac{1}{2}$ feet. which garden has a greater perimeter? how much greater is it?
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Explanation:

Step1: Calculate beet garden perimeter

Perimeter of square: $4 \times \text{side length}$
First convert mixed number: $12\frac{2}{3} = \frac{38}{3}$
Expression: $4 \times \frac{38}{3} = \frac{152}{3} = 50\frac{2}{3}$ feet

Step2: Compare perimeters

Beet garden perimeter: $50\frac{2}{3}$ ft, squash garden: $50\frac{1}{2}$ ft
Expression: $50\frac{2}{3} > 50\frac{1}{2}$

Step3: Find difference in perimeters

Convert to common denominator (6): $50\frac{4}{6} - 50\frac{3}{6}$
Expression: $50\frac{4}{6} - 50\frac{3}{6} = \frac{1}{6}$ feet

Answer:

The beet garden has a greater perimeter, by $\frac{1}{6}$ feet.