Answer: x = 26 cm.
Explanation:
Let x = the length of the rectangle
The area of a rectangle is the length times the width, so we can set up the equation:
56 cm^2 = x(2x - 5)
Expand the parentheses and solve for x:
56 cm^2 = 2x^2 - 5x
Add 5x to both sides:
2x^2 + 5x = 56 cm^2 + 5x
Subtract 56 cm^2 from both sides:
2x^2 = 5x + 56 cm^2
Divide both sides by 2:
x^2 = 5x/2 + 28 cm^2
Subtract 5x/2 from both sides:
x^2 - 5x/2 = 28 cm^2
Factor the left side:
x(x - 5/2) = 28 cm^2
Divide both sides by (x - 5/2):
x = 28 cm^2 / (x - 5/2)
Since we know that x is the length of the rectangle, and the length is 2 cm more than x, we can substitute x + 2 for x:
x + 2 = 28 cm^2 / (x + 2 - 5/2)
Simplify the right side:
x + 2 = 28 cm^2 / (x + 1)
Multiply both sides by (x + 1):
x + 2 = 28 cm^2
Subtract 2 from both sides:
x = 26 cm^2
Therefore, the length of the rectangle is 26 cm, and the width is 5 cm less than twice x, or 5 cm less than 52 cm, or 47 cm.
The answer is x = 26 cm.