Final answer:
To determine the dimensions of the rectangle, the width is calculated using the perimeter formula and the given relation between length and width. The width is found to be 4.8 cm. Substituting this value back into the relationship, the length is determined to be 15 cm, corresponding to option b: length = 15 cm; width = 4.8 cm.
Step-by-step explanation:
To solve for the dimensions of the rectangle, we have been given the perimeter and a relationship between its length and width. Let's call the width of the rectangle w and then the length, according to the given information, would be 5.4 cm + 2w.
The perimeter (P) of a rectangle is calculated by the formula P = 2l + 2w, where l is the length and w is the width of the rectangle. Plugging the given perimeter of 39.6 cm into this equation, we get:
39.6 = 2(5.4 + 2w) + 2w
39.6 = 10.8 + 4w + 2w
39.6 = 10.8 + 6w
28.8 = 6w
w = 4.8 cm
Now that we have the width, we can find the length using the relationship given initially:
Length = 5.4 cm + 2(4.8 cm) = 5.4 cm + 9.6 cm = 15 cm
Therefore, the dimensions of the rectangle are: length = 15 cm and width = 4.8 cm, which corresponds to option b.