Answer: Let the width of the rectangle be w and the length be l. We are given that the area of the rectangle is 45 cm^2, so we can write the equation:
w * l = 45
To find the lengths of the sides, we need to solve for w and l. We can divide both sides of the equation by any non-zero number to find an equivalent expression. For example, we can divide both sides by 9:
(w/9) * (l/9) = 45/9
Simplifying, we get:
w/9 * l/9 = 5
So, w/9 = 5/l and w = 5l/9.
Substituting the expression for w into the original equation, we get:
(5l/9) * l = 45
Expanding and simplifying, we get:
5l^2/9 = 45
Multiplying both sides by 9, we get:
5l^2 = 405
Dividing both sides by 5, we get:
l^2 = 81
Taking the square root of both sides, we get:
l = 9
So, the length of the rectangle is 9 cm. To find the width, we can substitute the value of l back into the expression we derived earlier:
w = 5l/9
w = 5 * 9 / 9
w = 5
So, the width of the rectangle is 5 cm.
The lengths of the sides of the rectangle, both exactly and approximately, are 9 cm and 5 cm.
Explanation: