Answer:
Explanation:
Let's denote the width of the rectangle as w (in cm). Then, according to the problem statement, the length of the rectangle is 1 and 2/3 times as long as its width, which can be written as:
length = (5/3) * width
We know that the area of the rectangle is 60 square centimeters, so we can write:
area = length * width
60 = (5/3) * w * w
60 = (5/3) * w^2
To solve for w, we can divide both sides by (5/3):
60 / (5/3) = w^2
36 = w^2
Taking the square root of both sides (note that w must be positive, so we can ignore the negative square root):
w = sqrt(36) = 6
So the width of the rectangle is 6 cm. Using the expression for the length in terms of the width, we can find the length:
length = (5/3) * width = (5/3) * 6 = 10
Therefore, the length and width of the rectangle are 10 cm and 6 cm, respectively.