Answer:
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
