Final answer:
Solving the provided relationship between the width and length of the rectangle and using the known area, we find that none of the answer options match the correct rectangle dimensions, which are found to be Length = 13 cm and Width = 24 cm.
Step-by-step explanation:
To find the dimensions of the rectangle given a relationship between the length and the width, and the maximum area of the rectangle.
We can form an equation using the information that the width (w) is 15 cm less than three times the length (l), which can be expressed as w = 3l - 15.
Since the area of a rectangle is the product of its length and width, we can write the equation for the area as l * (3l - 15) = 78 cm².
After simplifying, we can solve the quadratic equation for l. We can then plug the value of l back into the width equation to find w.
Solving the equation, we get:
- l * (3l - 15) = 78
- 3l^2 - 15l - 78 = 0
- Factoring, we find (3l + 6)(l - 13) = 0; hence l = 13 cm
- w = 3*13 - 15 = 39 - 15 = 24 cm
Therefore, the correct dimensions of the rectangle are Length = 13 cm and Width = 24 cm, which does not match any of the options provided.