Final answer:
To find the length of the table, we set up an equation using the given information and solve for x by simplifying and taking the square root. The length of the table is approximately 68.46 units.
Step-by-step explanation:
To solve this problem, we can set up an equation using the given information. Let the length of the table be represented by 'x'. According to the problem, the width is 0.74 times the length. So the width can be represented as 0.74x. The area of a rectangle is found by multiplying its length and width, so we can set up the equation: x * 0.74x = 3468.
Simplifying the equation, we get 0.74x^2 = 3468. To solve for x, divide both sides of the equation by 0.74: x^2 = 3468 / 0.74. x^2 = 4680. Now take the square root of both sides to find x: x = √4680.
Using a calculator, we find that x ≈ 68.46. Therefore, the length of the table is approximately 68.46 units.