A rectangle has area 16m2 . Express the perimeter of the rectangle as a function of the length of one of its sides.

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soniarus7x · Accepted Answer

Two variables are required to represent a rectangle&#039;s sides. Let&#039;s decide on x for width and y for length. Knowing that the rectangle&#039;s area is 16, we can now represent it.xy=16&amp;nbsp;y=16x&amp;nbsp;Perimeter of a rectangle.&amp;nbsp;P=2x+2y&amp;nbsp;P=2x+2(16x)&amp;nbsp;P=2x+32x&amp;nbsp;P=2x2+32x&amp;nbsp;Note that the domain will be x&amp;gt;0 as the width must be positive. If the length is larger than the width then the domain will be 0&amp;lt;x&amp;lt;4 which can be seen as follows:&amp;nbsp;16x&amp;gt;x⇒16&amp;gt;x2⇒x&amp;lt;4.&amp;nbsp;Answer:&amp;nbsp;P=2x2+32x

madeleinejames20 · Accepted Answer

Step 1:Let l represent the length of one side of the rectangle.The area of the rectangle is given by A=l·w, where w represents the width.Given that the area is 16m2, we have the equation 16=l·w.Step 2:To express the perimeter of the rectangle as a function of the length, we need to find the value of w in terms of l.Solving the equation for w, we have w=16l.The perimeter of a rectangle is given by P=2(l+w).Substituting the value of w, we get P=2(l+16l).Therefore, the perimeter of the rectangle as a function of the length of one of its sides is P(l)=2(l+16l).

Eliza Beth13 · Accepted Answer

Let&#039;s denote the length of one side of the rectangle as x (in meters).The area of a rectangle is given by the formula A={length}×{width}. In this case, we have the area A=16{m}2. Since we are considering a rectangle, the length and width are equal to x.Thus, we can write the equation for the area of the rectangle as x×x=16{m}2. Simplifying this equation, we get x2=16{m}2.To find the length of one side, we need to take the square root of both sides of the equation. Since the length cannot be negative in this context, we consider only the positive square root. Therefore, we have x=16{m}.Simplifying the square root, we get x=4{m}.Now, let&#039;s express the perimeter of the rectangle as a function of the length of one of its sides. The perimeter of a rectangle is given by the formula P=2×({length}+{width}).In this case, the length and width are both equal to x. Substituting x with 4{m}, we can write the formula for the perimeter as P=2×(4{m}+4{m}).Simplifying the expression inside the parentheses, we get P=2×8{m}.Finally, evaluating the multiplication, we find P=16{m}.Hence, the perimeter of the rectangle is given by the function P(x)=16{m}.

Nick Camelot · Accepted Answer

Result:P(x)=2x+32xSolution:The area of a rectangle is given by the formula: A={length}×{width}. In this case, we know that the area is 16 square meters, so we can write the equation as:16=x×{width}To express the perimeter of the rectangle as a function of the length of one of its sides, we need to find the width of the rectangle.To find the width, we can rearrange the equation by dividing both sides by x:16x={width}The perimeter of a rectangle is given by the formula: P=2×{length}+2×{width}.Using the values we have, the perimeter can be expressed as:P=2x+2×16xSimplifying further, we get:P=2x+32xHence, the perimeter of the rectangle is expressed as the function P(x)=2x+32x.

A rectangle has area 16 m^{2} . Express the perimeter

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