Kasia plants her watermelons in rows. Her watermelon field has a perimeter of 71 1/3 yards and is 44 feet wide. The rows will be planted 2 2/3 yards apart. How many rows of watermelons can she plant
Answer with explanation:
Perimeter of watermelon field \(=71\frac{1}{3}\) yard
1 yard =3 feet
So, perimeter
\(=71 \frac{1}{3}*3=\frac{214}{3}*3=214\)feet
Width of Watermelon field = 44 feet
Kaisa , plants watermelon in the field in rows which are \(=2\frac{2}{3}=\frac{8}{3}\) feet apart.
Number of watermelon planted in a single row =x
Let , Length of Watermelon field
\(=\frac{8(x-1){\text{feet}}}{3}\)
Perimeter of field = 2 *[Length +Breadth]
\(214=2*[44+\frac{8(x-1)}{3}]\\\\\frac{214}{2}=44+\frac{8(x-1)}{3}\\\\107-44=\frac{8(x-1)}{3}\\\\63=\frac{8(x-1)}{3}\\\\x-1=\frac{3*63}{8}\\\\x=\frac{189}{8}+1\\\\x=\frac{197}{8}\\\\x=24\frac{5}{8}\)
Number of watermelon in a row =24(approx)
Length of watermelon field
\(=\frac{8}{3}*\frac{197}{8}=65\frac{2}{3}\) feet
Let number of rows of watermelon = y
\(\frac{197y}{8}=44\\\\ y=\frac{352}{197}=1.7860\)
= 2 Rows(approximately)