To find the width of Averi's area model, we start with the individual areas of the rectangles that represent the terms in the polynomial. We know that the height of the rectangles is 4, and we want to determine the width of the entire rectangle.
Averi's area model shows three rectangles with given areas:
- The first rectangle has an area of \(4x^2\).
- The second rectangle has an area of \(20x\).
- The third rectangle has an area of \(-16\).
Since the area of each rectangle is given by the formula:
\[ \text{Area} = \text{Height} \times \text{Width} \]
we can set up equations to find the widths of each rectangle.
Finding Individual Widths:
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For the first rectangle: \[ 4 \times \text{Width}_1 = 4x^2 \implies \text{Width}_1 = \frac{4x^2}{4} = x^2 \]
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For the second rectangle: \[ 4 \times \text{Width}_2 = 20x \implies \text{Width}_2 = \frac{20x}{4} = 5x \]
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For the third rectangle: \[ 4 \times \text{Width}_3 = -16 \implies \text{Width}_3 = \frac{-16}{4} = -4 \]
Combining the Widths:
The total width of the area model is the sum of the widths of the individual rectangles: \[ \text{Total Width} = \text{Width}_1 + \text{Width}_2 + \text{Width}_3 \] Substituting in the width values: \[ \text{Total Width} = x^2 + 5x - 4 \]
Thus, the width of Averi's area model is: \[ \boxed{x^2 + 5x - 4} \]