QuestionFind the perimeter of a rectangle with area $100 \mathrm{~m}^{2}$ as a function of one side's length.

Studdy Solution

STEP 1

Assumptions1. The area of the rectangle is100 square meters. . The length of one side of the rectangle is denoted by x.
3. The formula for the area of a rectangle is A = length * width.
4. The formula for the perimeter of a rectangle is =*(length + width).
5. The width of the rectangle can be expressed as a function of its area and length.

STEP 2

First, we need to express the width of the rectangle as a function of its area and length. We can do this by rearranging the formula for the area of a rectangle.
$Width = Area / Length$

STEP 3

Now, plug in the given values for the area and the length to express the width as a function of the length.
$Width =100 / x$

STEP 4

Now that we have the width as a function of the length, we can express the perimeter of the rectangle as a function of the length. We can do this by substituting the expression for the width into the formula for the perimeter of a rectangle.
$Perimeter =2 * (Length + Width)$ $Perimeter =2 * (x +100 / x)$

STEP 5

implify the expression for the perimeter.
$Perimeter =2x +200 / x$ The perimeter of the rectangle is a function of the length of one of its sides and can be expressed as(x) =2x +200 / x.

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