Question

The area of a rectangle is 56 cm. The length is 2 cm more than x and the width is 5 cm less than

Answer 1

Answer:

x = 6, length = 8 cm and width = 7 cm

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