Question

AMMY has 280 meters of fencing and wishes to form three sides of a rectangular field. the fourth side borders a river and will not need fencing. as shown below, one of the sides has length x (in meters). find a function that gives the area a(x) of the field in terms of x?

Answer 1

The function that gives the area A(x) of the field in terms of x is A(x) = 140x - x²/2, where x represents the length of the side along the river, and 280 meters is the total amount of fencing used for the remaining three sides.

Step-by-step explanation:

The student is asking how to represent the area of a rectangular field as a function of one of its sides, given a fixed amount of fencing for three of the sides. Since AMMY has 280 meters of fencing and wants to use this fencing for three sides of a rectangular field, with one side along the river not requiring fencing, we can express this situation with the following relations:

The area A(x) of the rectangular field can be found by multiplying the length of one side along the river (which is x) by the length of one of the adjacent sides, which is (280 - x)/2.

Therefore, the area function is:

A(x) = x × (280 - x)/2

A(x) = x/2 × (280 - x)

A(x) = 140x - x2/2