The area of a tabletop is 48 square feet. The length is 3 times the width. If the dimensions are whole numbers, what is the width of the tabletop
A = LW
48 = 3W * W
48 = 3W^2
16 = W^2
4 = W
To find the width of the tabletop, we can use the information given about the area and the relationship between the length and the width. Here's how we can solve it step by step:
1. Let's assume the width of the tabletop is x.
2. According to the problem, the length is 3 times the width, which means the length would be 3x.
3. The area of a rectangle is calculated by multiplying the length and width. In this case, the area is given as 48 square feet, so we have the equation: x * 3x = 48.
4. Simplifying the equation, we get: 3x^2 = 48.
5. Divide both sides of the equation by 3 to isolate x^2: x^2 = 48/3.
6. Simplify the right side: x^2 = 16.
7. To solve for x, take the square root of both sides: √(x^2) = √16.
8. The square root of 16 is 4 (since 4 * 4 = 16).
9. Therefore, the width of the tabletop is x = 4.
So, the width of the tabletop is 4 feet.