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gina has 480 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed area. What is the maximum​ area?

Sagot :

evgeniylevi

Answer:

14400 [yards²].

Step-by-step explanation:

all the details are in the attached picture; answer is marked with orange colour.

note, the suggested way of solution is not the shortest one, modify the design according Your local requirements.

P.S. ∡ means 'if', ⇒ means 'then'.

View image evgeniylevi
mhanifa

Answer:

  • 14400 yd²

Step-by-step explanation:

Fencing is the perimeter of rectangle:

  • P = 2(l + w) = 480

The sum of dimensions is:

  • l + w = 240 yd

The area is the product of two dimensions:

  • A = lw
  • A = l(240 - l) = 240l - l²

This a quadratic relationship and the maximum value is obtained at vertex.

The vertex is the point:

  • l = -b/2a = -240/ -2 = 120

It means both l and w have same length of 120 yd

The area is:

  • A = 120*120 = 14400 yd²
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