Question

a rectangular vineyard has 2,000 grapevines that are planted with a spacing of 4 square meters per grapevine. the vineyard has a fixed width of 64 meters.

1. what is the area of the vineyard?
2. what is the length of the vineyard?

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1. the area of the vineyard is square meters.
2. the length of the vineyard is meters.

Explanation:

Step1: Calculate the area of the vineyard

The number of grapevines is \(n = 2000\) and the area per grapevine is \(a=4\) square meters.
The area of the vineyard \(A\) is the product of the number of grapevines and the area per grapevine.
\(A=n\times a\)
\(A = 2000\times4\)
\(A=8000\) square meters

Step2: Calculate the length of the vineyard

The formula for the area of a rectangle is \(A = l\times w\), where \(A\) is the area, \(l\) is the length and \(w\) is the width.
We know that \(A = 8000\) square meters and \(w = 64\) meters.
To find \(l\), we use the formula \(l=\frac{A}{w}\)
\(l=\frac{8000}{64}\)
\(l = 125\) meters

Answer:

1. \(8000\)
2. \(125\)