Let's call x to the length of the rectangle and y to its width, then, from the given information we can formulate the following equations:
Since the length "x" equals 8 times more than two times the width "y", we just have to add 8 to the product of y and 2 and then make it equal to x, then we get:
x = 8 + 2×y
We can also formulate another equation, that is the perimeter of the rectangle, the perimeter of a rectangle is given by the following expression:
P = 2y + 2x
In this case, P equals 40, by replacing 40 for P and 8 + 2y into the above equation, we get:
40 = 2y + 2(8 + 2y)
40 = 2y + 2×8 + 2×2y
40 = 2y + 16 + 4y
Combining like terms:
40 = 6y + 16
Solving for y:
40 -16 = 6y + 16 - 16
24 = 6y
24/6 = 6y/6
4 = y
y = 4
Then y equals 4. In order to find the value of x, we just have to replace 4 for y into the equation x = 8 + 2×y, like this:
x = 8 + 2×4
x = 8 + 8
x = 16
Then, x equals 16 and y equals 4. Since x represents the length and y represents the width, then the length of the rectangle equals 16 cm and its width equals 4.