Final answer:
The width of the rectangular frame is 7 centimeters, and the length is 41 centimeters, found by setting up an equation using the given perimeter and the relationship between the length and width.
Step-by-step explanation:
Rashau wants to find the dimensions of a rectangular frame for her oil painting.
The length of the rectangular frame is said to be 20 centimeters more than triple the width, and the perimeter of the frame is given to be 96 centimeters.
To solve this, we will use the formula for the perimeter of a rectangle, P = 2L + 2W, where P stands for the perimeter, L for the length, and W for the width.
- Let the width of the frame be W centimeters.
- Then, the length will be 3W + 20 centimeters.
- Writing the equation for the perimeter: 96 = 2(3W + 20) + 2W.
- Simplifying the equation: 96 = 6W + 40 + 2W.
- Combining like terms: 96 = 8W + 40.
- Subtracting 40 from both sides: 56 = 8W.
- Dividing by 8: W = 7 centimeters.
- Finding the length: L = 3(7) + 20 = 41 centimeters.
So, the width of the frame is 7 centimeters, and the length is 41 centimeters.