Help...............

Question

Gerry Anium is designing a rectangular garden. It will sit next to a long, straight rock wall, thus leaving only three sides to be fenced. Gerry has bought 150 feet of fencing in one-foot sections. Subdivision into shorter pieces is not possible. The garden is to be rectangular and the fencing (all of which must be used) will go along three of the sides as indicated in the picture.

o----------------------

o I wall-> o

o I

o garden I

o I

o----------------------

(a) If each of the two sides attached to the wall were 40 ft long, what would the length of the third side be?

(b) Let x be the length of the side parallel to the wall. Find the lengths of the other two sides, in terms of x.

(c) Express the area of the garden as a function of x, and graph this function. For what values of x does this graph have meaning?

(d) Gerry would like to enclose the largest possible area possible with this fencing. What dimensions for the garden accomplish this? What is the largest possible area?

Answer 1

(a) 150 - 40 - 40 = ?

(b) (150 - x) / 2 = ?

(c) A(x) = x((150 - x) / 2)

(d) A(x) = (150x - x²) / 2, Can you convert to vertiex form and answer?