16. The area of the rectangle is 5x2 + 17x + 6. Find the length & width (the factors), then determine the perimeter of the rectangle.Length:Width:Perimeter:

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asked May 4, 2023 141k views

1 Answer

Gareth Lewis · Answer 1 · 2023-05-10T19:46:53+0000

Area of a rectangle is represented by the expression:

$\text{Area}=\text{length }\cdot\text{ width}$

Since, the area is defined by the following expression:

$\begin{gathered} \text{Area}=5x^2+17x+6 \\ We\text{ can factor the expression:} \\ \text{Area}=(5x+2)(x+3) \end{gathered}$

So, notice that:

$\begin{gathered} \text{Length}=5x+2 \\ \text{Width}=x+3 \end{gathered}$

The perimeter is given by the following formula:

$\begin{gathered} \text{Perimeter}=2L+2W \\ \text{Perimeter}=2(5x+2)+2(x+3) \\ \text{Perimeter}=10x+4+2x+6 \\ \text{Perimeter}=12x+10 \end{gathered}$