Suppose the lengths of the four side of a quadrilateral are represented by the expressions 3a, a+2, 2a-1, and 3a+6. write the sum of the lenghts (the perimeter), and then simplify.
To find the sum of the lengths (perimeter) of a quadrilateral, you need to add up the lengths of all four sides. In this case, the lengths are represented by the expressions 3a, a+2, 2a-1, and 3a+6.
So, to find the perimeter, we add these four expressions together:
Perimeter = 3a + (a+2) + (2a-1) + (3a+6)
Now, let's simplify the expression:
Perimeter = 3a + a + 2 + 2a - 1 + 3a + 6
Combine like terms: (3a + a + 2a + 3a) + (2 - 1 + 6)
Perimeter = 9a + 7
Therefore, the sum of the lengths (perimeter) of the quadrilateral is 9a + 7.