Final answer:
To find the rectangle dimensions, a linear system is formed using the perimeter formula and the relationship between length and width. Upon solving, the rectangle's dimensions are determined to be a length of 7 cm and a width of 2 cm.
Step-by-step explanation:
Solving the Linear System for Rectangle Dimensions
Lets define the variables for the rectangle where l represents the length and w represents the width. Given that the perimeter of the rectangle is 18 cm, we can state the perimeter formula as 2l + 2w = 18. Additionally, we are told that the length is 5 cm greater than the width, which gives us the equation l = w + 5.
Now, we will use substitution to solve for the width and length:
- Substitute l = w + 5 into the perimeter equation: 2(w + 5) + 2w = 18.
- Simplify: 2w + 10 + 2w = 18.
- Combine like terms: 4w + 10 = 18.
- Isolate w: 4w = 18 - 10, which simplifies to 4w = 8.
- Divide by 4: w = 2 cm.
Since we now know that w = 2 cm, we can find the length by substituting back into the equation l = w + 5:
- Substitute w into the equation for l: l = 2 + 5.
- Thus, l = 7 cm.
Therefore, the dimensions of the rectangle are: length is 7 cm and width is 2 cm.