A farmer will build a fence around a rectangular parcel of land.

The length l = 321 feet and the width w = 210 feet are given.

Find the total cost of the fence, assuming that such a fence costs $1.50 per yard.

Round to the nearest whole number and then enter numeric values without units and symbols.

Example: If the cost is 89 dollars, enter 89 as your answer.

Question

A farmer will build a fence around a rectangular parcel of land.

The length l = 321 feet and the width w = 210 feet are given.

Find the total cost of the fence, assuming that such a fence costs $1.50 per yard.

Round to the nearest whole number and then enter numeric values without units and symbols.

Example: If the cost is 89 dollars, enter 89 as your answer.

BlackTom AI · Accepted Answer

Begin by identifying the given dimensions and the cost structure. The fence must enclose a rectangle with length l = 321 ft and width w = 210 ft, so the perimeter in feet is P = 2(l + w).

Compute the sum of length and width: l + w = 321 + 210 = 531 ft. Doubling that for the full perimeter gives P = 2 × 531 = 1062 ft.

Next, convert the perimeter from feet to yards since the cost is per yard. There are 3 feet in a yard, so the perimeter in yards is P_yards = 1062 ÷ 3 = 354 yd.

Now apply the cost per yard. At $1.50 per yard, the total cost is Cost = 354 × 1.50.

Perform the multiplication: 354 × 1.50 = 354 × (3/2) = (354 × 3) / 2 = 1062 / 2 = 531. Since the instruction asks for the nearest whole number and the calculation yields an exact integer, no rounding changes are necessary.

Thus, the calculated total cost in dollars is 531.0, expressed as a whole number when entered without units or symbols.

ST-MATH-0824-750-49498-202503 Q4 Geometry & Voting

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