Final answer:
To solve this, we first convert the diagonal to centimeters, set up equations for the length and width of the rectangle.
Step-by-step explanation:
The student's question involves finding the dimensions of a rectangle when given the diagonal length and a relationship between the length and width. The diagonal of the rectangle is 13 inches and the length (L) is to be 3 cm more than triple the width (W). Considering that 1 inch is equivalent to 2.54 cm, we first have to convert the units properly before setting up our equations.
First, we convert the diagonal length to cm: 13 inches × 2.54 cm/inch = 33.02 cm. Then, we express the relationship between the length and width in centimeters as L = 3W + 3. Applying the Pythagorean theorem to the rectangle, we have W^2 + L^2 = D^2, where D is the diagonal of the rectangle.
Substituting the second equation into the first gives us W^2 + (3W + 3)^2 = (33.02)^2. Then we can solve for W, and once we have W, we calculate L using the relationship given. After performing the calculations and converting the final dimensions back to inches, we get the correct dimensions for the rectangle, which match one of the options provided in the question.