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Suppose that the length of a rectangle is one and two-thirds times as long as its width. The area of the rectangle is 60 square centimeters. Find the length and width of the rectangle.

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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.

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