Ask Question
6 May, 19:53

Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 392 meters

+1
Answers (1)
  1. 6 May, 21:08
    0
    the length is 98 meters and the width 98 meterss

    Step-by-step explanation:

    We have that the length is l and the width is w, we know that:

    P = 2 * w + 2 * l

    if we solve for it, we have:

    l = P / 2 - w

    Now, we know that the area is:

    A = l * w

    if we replace l, we are left with:

    A = (P / 2 - w) * w

    A = P * w / 2 - w ^ 2

    we derive to know the maximum area and we equal 0 and we have:

    A ' = P / 2 - 2 * w

    0 = P / 2 - 2 * w

    w = P / 4

    now for him:

    l = P / 2 - P / 4

    l = P / 4

    Therefore, if we replace:

    l = 392/4 = 98

    w = 392/4 = 98

    For the maximum area the length is 98 meters and the width 98 meterss
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 392 meters ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers