Ask Question
24 January, 11:56

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

+2
Answers (1)
  1. 24 January, 13:04
    0
    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
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “What is the length and width of a rectangle given by the trinomial r squared - 6r - 55? Use factoring ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers