Final answer:
To find the dimensions of the rectangle, we used the perimeter formula and the relationship between the length and the width. The width was found to be 2cm and the length 10cm.
Step-by-step explanation:
The student has been tasked with determining the dimensions of a rectangle given that the length is 4cm more than three times the width and the perimeter is 24cm. To solve this, we will let the width be represented as 'w' and the length as 'l'. Since the length is 4cm more than three times the width, we can express this as l = 3w + 4. The perimeter of a rectangle is given by the formula P = 2l + 2w. By substituting the given perimeter and the expression for the length into this formula, we will be able to solve for 'w' and subsequently for 'l'.
Solving the Equation
- Start with the perimeter formula: P = 2l + 2w.
- Substitute the given perimeter and expression for the length: 24 = 2(3w + 4) + 2w.
- Simplify and solve for 'w': 24 = 6w + 8 + 2w → 24 = 8w + 8 → 16 = 8w → w = 2.
- Now substitute 'w' back into the equation for the length to find 'l': l = 3(2) + 4 = 6 + 4 = 10.
Thus, the width of the rectangle is 2cm, and the length is 10cm.