Question

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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

Answer 1

The results are the opposite sign of x1 and x2.

`lenght \: = (x - 8) \: and \: width \: = (x - 9)`

Explanation:

`{x}^(2) - 17x + 72 = 0`

`Δ = {(17)}^(2) - 4(1 * 72)`

`Δ = 289 - 288 = 1`

`x1 \: and \: x2 = (17± √(1))/(2)`

`x1 = (17 + 1)/(2) = 9`

`x2 = (17 - 1)/(2) = 8`