Express the given quantity as a function of one variable .
the perimeter of a rectangle of length and width that has an area of 192 square meters

Ask by Wade Ray. in the United States

Mar 24,2025

Question

Express the given quantity as a function $$ f(x) $$ of one variable $$ x $$. the perimeter of a rectangle of length $$ x $$ and width $$ y $$ that has an area of 192 square meters $$ f(x)=\square $$

UpStudy AI · Accepted Answer

1. The area of the rectangle is given by
   $$
   xy = 192.
   $$
   Solving for $$ y $$ in terms of $$ x $$, we have
   $$
   y = \frac{192}{x}.
   $$

2. The perimeter of the rectangle is given by
   $$
   P = 2x + 2y.
   $$
   Substituting $$ y = \frac{192}{x} $$ into the perimeter formula, we obtain
   $$
   P = 2x + 2\left(\frac{192}{x}\right) = 2x + \frac{384}{x}.
   $$

Thus, the function $$ f(x) $$ that expresses the perimeter in terms of $$ x $$ is
$$
f(x)=2x+\frac{384}{x}.
$$
$$ f(x) = 2x + \frac{384}{x} $$

Express the given quantity as a function of one variable .
the perimeter of a rectangle of length and width that has an area of 192 square meters

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Express the given quantity as a function of one variable . the perimeter of a rectangle of length and width that has an area of 192 square meters