Final answer:
The perimeter equation was set up, simplified, and solved for 'x', and then the value of 'x' was substituted back into the width expression to find that the missing width of the rectangle is 26 cm.
Step-by-step explanation:
The problem is asking to find the missing value of the width of a rectangle when the length is given as 4 cm, the width is in the form of an expression (3x+2 cm), and the perimeter is provided as 60 cm. To solve this, we use the formula for the perimeter of a rectangle which is P = 2l + 2w. In this case, we have:
- P (perimeter) = 60 cm
- l (length) = 4 cm
- w (width) = 3x + 2 cm
Substitute the known values into the perimeter formula:
60 = 2(4) + 2(3x + 2)
60 = 8 + 2(3x + 2)
Now we will simplify and solve for x:
60 = 8 + 6x + 4
60 = 12 + 6x
48 = 6x
x = 8
Now that we have the value of x, we can find the missing value of the width:
w = 3x + 2
w = 3(8) + 2
w = 24 + 2
w = 26 cm
So, the missing value of the width of the rectangle is 26 cm.