Similar Example Video (1 point) A rectangular playground is to be fenced off and

Question

Similar Example Video (1 point) A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 460 feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. Remember to reduce any fractions and simplify your answers as much as possible. HINT Start by drawing a picture that illustrates what is being described in the problem, then label the important parts. Get help entering answers See a similar example (.PDF) The shorter side of the playground is The longer side of the playground is What is the maximum area? SE ft … ft. square ft.

Explanation / Answer

Let the shorter and longer sides are S and L

Fencing length = perimeter of the ground + S

(it really doesn't matter whether you take S or L here, the area enclosed will be same so you should take S in order to provide more for L)

Fencing length = 460 = 2(S+L) + S = 3S + 2L

To maximize area = S*L = S (230- 1.5S)

at maximum area, w.r.t. S, the first derivative of the area will be 0.

A' = 230 - 3S = 0

S = 230/3 = 76.67

L = 230 - 1.5*230/3 = 230/2 = 115

so area = 230/3*230/2 = 8816.67

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.