A rectangle has area 25 m2. express the perimeter of the rectangle as a function of the length l of one of its sides. p(l) = sta

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A rectangle has area 25 m2. express the perimeter of the rectangle as a function of the length l of one of its sides. p(l) = sta

te the domain of p. (assume the length of the rectangle is larger than its width. enter your answer using interval notation.)

Mathematics

1 answer:

zzz [12.3K] · Answer 1 · 2026-02-22T16:23:08+03:00

a) The area of a rectangle is calculated by multiplying the length by the width:
A = l·w

This formula allows us to express the width in terms of area and length. By dividing A by l, we find
A/l = w

We also recognize that the perimeter of a rectangle is the total length around it.
P = l + w + l + w
P = 2(l + w)
We aim to rewrite the perimeter formula to isolate l on one side, using the expression for w derived earlier.
P = 2(l + A/l)

By substituting the known value for A, we can express p(l) as
p(l) = 2(l + 25/l)
p(l) = 2l + 50/l

b) For lengths exceeding widths, we have
l > w
l > A/l
l² > A
l > √A
l > √25

This indicates that the domain of p(l) is
l ∈ (5, ∞)..... meters

A rectangle has area 25 m2. express the perimeter of the rectangle as a function of the length l of one of its sides. p(l) = sta

1)

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