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A rectangle has an area of (x2 − 17x + 72) square units. Since the area of a rectangle is determined using the formula, A = lw, what could be the length and width of the rectangle?

length = (x − 8) units and width = (x − 9) units
length = (x + 9) units and width = (x + 8) units
length = (x − 6) units and width = (x − 12) units
length = (x + 12) units and width = (x + 6) units

Respuesta :

Smokey263

Answer:

The results are the opposite sign of x1 and x2.

[tex]lenght \: = (x - 8) \: and \: width \: = (x - 9)[/tex]

Step-by-step explanation:

[tex] {x}^{2} - 17x + 72 = 0[/tex]

[tex]Δ = {(17)}^{2} - 4(1 \times 72)[/tex]

[tex]Δ = 289 - 288 = 1[/tex]

[tex]x1 \: and \: x2 = \frac{17± \sqrt{1}}{2} [/tex]

[tex]x1 = \frac{17 + 1}{2} = 9[/tex]

[tex]x2 = \frac{17 - 1}{2} = 8[/tex]

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