Answer:
<u>x = 6, length = 8 cm and width = 7 cm</u>
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Area of a rectangle = 56 cm²
Length of the rectangle = x + 2
Width of the rectangle= 2x - 5
2. Solve for x. Round to the nearest whole number.
Area of a rectangle = Length * Width
(x + 2) (2x - 5) = 56
2x² + 4x - 5x -10 = 56
2x² - x - 66 = 0
Factoring, we have:
(2x + 11) * (x - 6) = 0
x₁ = 2x + 11 = 0 ⇒ 2x = -11; x₁ = - 5.5
x₂ = x - 6 = 0 ⇒ x₂ = 6
We picked x₂ because x₁ will give us negative values for length and width.
Length = 6 + 2 = 8 cm
Width = 2 * 6 - 5 = 12 - 5 = 7 cm
