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Pavlova-9 [17]
1 year ago
9

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

ectangle.Length:Width:Perimeter:

Mathematics
1 answer:
Bezzdna [24]1 year ago
3 0

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}

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