Final answer:
To determine the dimensions of a rectangle with a perimeter of 86 cm, where the length is 4 cm more than twice its width, we use the perimeter formula, set up an equation, solve for the width, and then find the length. The width is found to be 13 cm and the length is 30 cm.
Step-by-step explanation:
To find the dimensions of a rectangle when given its perimeter, we need to set up and solve equations based on the rectangle's properties. The problem states that the rectangle's length (L) is 4 cm more than twice its width (W), and the rectangle has a perimeter of 86 cm. We represent this information mathematically as:
L = 2W + 4
and since the perimeter (P) of a rectangle is given by the formula P = 2L + 2W, we can substitute the given perimeter and the expression for L into this formula and solve for W, then use the value of W to find L.
The steps are as follows:
- Write the equation for the perimeter: 86 = 2(2W + 4) + 2W
- Simplify and solve for W: 86 = 4W + 8 + 2W → 86 = 6W + 8 → 78 = 6W → W = 13
- Plug the value of W into the length expression: L = 2(13) + 4 = 26 + 4 = 30
Therefore, the width of the rectangle is 13 cm and the length is 30 cm.