Question

The ratio of the length of a rectangle to its width is 7 : 2. If the perimeter of the rectangle is 108 centimeters, what are the dimensions of the rectangle?

Answer 1

42 centimeters for the length and 12 centimeters for the width.

Explanation:

Let's assume that the length of the rectangle is 7x and the width is 2x, where x is a common factor.

The perimeter of a rectangle is given by the formula: P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.
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Given that the perimeter of the rectangle is 108 centimeters, we can write the equation as:

108 = 2(7x + 2x).

Simplifying the equation:

108 = 2(9x).

54 = 9x.

x = 6.

Now, we can find the dimensions of the rectangle:

Length = 7x = 7 * 6 = 42 centimeters.

Width = 2x = 2 * 6 = 12 centimeters.

Therefore, the dimensions of the rectangle are 42 centimeters for the length and 12 centimeters for the width.