Question

To line the edges of a rectangular table cloth, 30 feet of lace are needed. The length of the table cloth is exactly one-half its width. What are the dimensions (length and width ) of the table cloth?

Answer 1

The length of the table cloth is half its width. Using the formula for the perimeter of a rectangle, we can solve for the dimensions of the table cloth. The dimensions are 5 feet by 10 feet.

Step-by-step explanation:

Let's first assign variables to represent the length and width of the table cloth. We can let L represent the length and W represent the width. We know that the length is half the width, so we can write an equation: L = (1/2)W.

We also know that the perimeter of the table cloth is 30 feet, and the formula for the perimeter of a rectangle is P = 2L + 2W. Substituting the value of L from the first equation, we can write: 30 = 2((1/2)W) + 2W.

Simplifying the equation, we get 30 = W + 2W. Combining like terms, we have 30 = 3W. Dividing both sides by 3, we find that W = 10 feet.

Finally, we can substitute this value back into the first equation to find the length: L = (1/2)(10) = 5 feet.

Therefore, the dimensions of the table cloth are 5 feet by 10 feet.

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