Solve the problem.
-Consider all rectangles with an area of $256 \mathrm {~cm} ^ { 2 }$. Let $x$ be the length of one side of such a rectangle. Express the perimeter as a function of $x$ and determine the dimensions of the rectangle that has the least perimeter.
A) $\mathrm { P } ( \mathrm { x } ) = 2 \mathrm { x } + \frac { 512 } { \mathrm { x } } ; 4 \mathrm {~cm} \times 64 \mathrm {~cm}$
B) $\mathrm { P } ( \mathrm { x } ) = \mathrm { x } + \frac { 256 } { \mathrm { x } } ; 16 \mathrm {~cm} \times 16 \mathrm {~cm}$
C) $\mathrm { P } ( \mathrm { x } ) = 256 \mathrm { x } ; 8 \mathrm {~cm} \times 32 \mathrm {~cm}$
D) $\mathrm { P } ( \mathrm { x } ) = 2 \mathrm { x } + \frac { 512 } { \mathrm { x } } ; 16 \mathrm {~cm} \times 16 \mathrm {~cm}$

Question

Quizplus · Accepted Answer

The correct perimeter function for a rectangle with area 256 cm² is $P(x) = 2x + \frac{512}{x}$, because the perimeter of a rectangle is given by $2(length + width)$, and if $x$ is one side and the area is $256$, the other side is $\frac{256}{x}$. The dimensions that minimize the perimeter are those of a square due to the properties of rectangles, which in this case is $16 \mathrm{~cm} \times 16 \mathrm{~cm}$.

Solve the Problem 256 cm2256 \mathrm {~cm} ^ { 2 }256 cm2 Let

Solve the Problem $256 \mathrm {~cm} ^ { 2 }$ Let