The equation is [tex]4x+ 3=18[/tex] and [tex]x = 4[/tex] cm.
Step-by-step explanation:
Step 1:
The perimeter of a rectangle is given by twice the sum of its length and its width.
The length of the given rectangle [tex]= x+1.5[/tex] cm.
The width of the given rectangle [tex]= x[/tex] cm.
The perimeter of the given rectangle [tex]= 2 (x+1.5+x) = 2 (2x+1.5).[/tex]
The perimeter of the rectangle is given as 19 cm.
Step 2:
By substituting the known values, we get
[tex]2 (2x+1.5) = 18 = 4x+ 3.[/tex] This is the equation.
[tex]4x = 19 -3 = 16, x = \frac{16}{4} =4.[/tex]
So [tex]x = 4[/tex] cm.
