What is the length and width of a rectangle given by the trinomial r squared - 6r - 55? Use factoring

The length and the width of the rectangle are 11 units and 5 units

Step-by-step explanation:

Let us use the factorization to find the length and the width of the rectangle

∵ The trinomial is r² - 6r - 55

∵ r² = (r) (r)

∵ - 55 = (-11) (5)

- Multiply r by - 11 and r by 5, then add the products, the sum

must be equal the middle term of the trinomial

∵ (r) (-11) = - 11r

∵ (r) (5) = 5r

∵ - 11r + 5r = - 6r ⇒ the middle term of the trinomial

∴ r² - 6r - 55 = (r - 11) (r + 5)

- Equate each factor by 0 to find the value of r

∵ r - 11 = 0

- Add 11 to both sides

∴ r = 11

OR

∵ r + 5 = 0

- Subtract 5 from both sides

∴ r = - 5 ⇒ rejected because no negative dimensions

∴ The length of the rectangle is 11 units

∵ The area of the rectangle is 55 units²

∵ Area of a rectangle = length * width

∴ 55 = 11 * width

- Divide both sides by 11

∴ 5 = width

∴ The width of the rectangle is 5 units