Question

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

Answer:  length = (x − 8) units and width = (x − 9) units

Explanation:

The area of the rectangle is

$x^2 -17 x + 72$

This is a second-order polynome of the form

$ax^2 + bx + c$ (1)

with b=-17 and c=72. This type of polynome can be decomposed into the form

$(x+a_1)(x+a_2)$

If we rewrite explicitely this last form, we have

$x^2 + a_1 x + a_2 x + a_1 a_2 = x^2 + (a_1 + a_2) x + a_1 a_2$ (2)

If we compare (1) with (2), we notice that they are exactly the same form, with:

$a_1 + a_2 = b$

$a_1 a_2 = c$

Since we know b=-17 and c=72, we have to find the two numbers $a_1$ and $a_2$ whose sum is -17 and whose product is 72. The two numbers must be both negative (since their product is positive and their sum is negative), so they are:

$a_1 = -8$

$a_2 = -9$

Therefore, the length and the width of the rectangle are

$(x-8)$

$(x-9)$

Answer 2

Answer:

its A

Step-by-step explanation: