The definition of congruent is that the sides are the same length or otherwise identical. This means that [tex]3x+21 = 4x+18[/tex]. From this, we can solve for x.
[tex]3x+21 = 4x+18[/tex]
Subtract 18 from both sides.
[tex]3x+3 = 4x[/tex]
Subtract 3x from both sides.
[tex]3 = x[/tex]
This means x is equal to 3.
The perimeter of a shape is the length of all sides added together. So the equation should be [tex]9 + (3x + 21) + (4x + 18) = P[/tex]. Since we know the value of x, we can plug that in and solve for P.
[tex]9 + (3(3) + 21) + (4(3) + 18) = P[/tex]
[tex]9 + (9 + 21) + (12 + 18) = P[/tex]
[tex]9 + (30) + (30) = P[/tex]
[tex]69 = P[/tex]
Thus, the perimeter of the shape is 69.
