Answer:
Let's denote the width of the rectangle as "w" and the length as "l."
According to the given information:
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, it is given as 54. So, we can write the equation:
2w + 2l = 54 (since a rectangle has two pairs of equal sides)
The length is 9 more than 2 times the width. Mathematically, this can be expressed as:
l = 2w + 9
Explanation:
Step 1: Substitute the value of l from equation 2 into equation 1.
2w + 2(2w + 9) = 54
Step 2: Simplify the equation by performing the multiplication.
2w + 4w + 18 = 54
Step 3: Combine like terms.
6w + 18 = 54
Step 4: Subtract 18 from both sides of the equation.
6w = 54 - 18
6w = 36
Step 5: Divide both sides of the equation by 6.
w = 36 / 6
w = 6
Now we have the width of the rectangle, which is 6.
Step 6: Substitute the value of w into equation 2 to find the length.
l = 2w + 9
l = 2(6) + 9
l = 12 + 9
l = 21
So, the width of the rectangle is 6 units, and the length is 21 units.