A farmer has determined that a crop of strawberries yields a yearly profit of $1.50 per square yard. If strawberries are planted on a triangular piece of land whose sides are 50 yards, 75 yards, and 100 yards, how much profit, to the nearest hundred dollars, would the farmer expect to make from this piece of land during the next harvest?
Multiply the area of the triangle by $1.50 per square yard.
There is a formula for the araa of a triangle using the lengths of the three sides. You could also use the law of cosines to get any of the angles of the triangle, and use that angle to get the altitude to use with some base, for the area.
square with sides of 18.3 m
2700
To calculate the profit the farmer would expect to make from the triangular piece of land, we first need to find the area of the triangle. Since the sides of the triangle are given as 50 yards, 75 yards, and 100 yards, we can use Heron's formula to find the area.
Heron's formula states that for a triangle with side lengths a, b, and c, the area (A) can be calculated using the formula:
A = sqrt(s * (s - a) * (s - b) * (s - c))
Where s represents the semiperimeter of the triangle, given by:
s = (a + b + c) / 2
Let's substitute the given values into the formulas to find the area of the triangle:
s = (50 + 75 + 100) / 2 = 225 / 2 = 112.5
A = sqrt(112.5 * (112.5 - 50) * (112.5 - 75) * (112.5 - 100))
A = sqrt(112.5 * 62.5 * 37.5 * 12.5)
A = sqrt(1738281.25)
A ≈ 1318.51 square yards
Now that we have the area of the triangle, we can calculate the expected profit. The profit per square yard is given as $1.50. So, to find the total profit, we multiply the profit per square yard by the area of the triangle:
Profit = $1.50 * 1318.51
Profit ≈ $1977.76
Therefore, the farmer would expect to make approximately $1977.76 in profit from this piece of land during the next harvest.