Math CentralQuandaries & Queries


Question from Julieta, a student:

The area of a field shaped like a triangle is 750yards squared. One leg of the field is fenced with wood costing $5/yd. The remainder of the perimeter of the field is fenced with steel costing $10/yd. The perimeter of the field is 150yards. the total cost of the fencing is $1200.
a. What is the length of the leg fenced with wood?
b. what is the length of the leg fenced with steel?


Suppose that the leg of the triangle to be fenced in wood is x yards long. Since the total perimeter is 150 yards the sum of the lengths of the other two sides must be 150 - x yards. The wood costs $5 per yard so putting a wooded fence along the side of length x yards will cost 5x dollars. The steel fencing costs $100 per yard so fencing the remaining two sides with steel fencing will cost 10(150 - x) dollars. The total cost for the fencing is $1200.

Can you complete the problem now?

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