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.
add up the four side for the perimeter. I will be happy to critique your work.
Is the answer 8a-1. If not, please help.
9a
To find the sum of the lengths (perimeter) of the quadrilateral, you need to add together the lengths of all four sides.
The lengths of the four sides are represented by the expressions: 3a, a+2, 2a-1, and 3a+6.
To get the sum, you simply add these four expressions:
(3a) + (a + 2) + (2a - 1) + (3a + 6)
Now, let's simplify the expression:
Combine like terms by adding or subtracting the coefficients (the numbers in front of the 'a'):
3a + a + 2 + 2a - 1 + 3a + 6
Group together the like terms:
(3a + 2a + 3a) + (a - 1) + (2 + 6)
Now, combine these terms:
8a + (a - 1) + 8
Simplify further:
8a + a - 1 + 8
Combine like terms: 8a + a = 9a:
9a - 1 + 8
Combine the constant terms: -1 + 8 = 7:
9a + 7
So, the simplified expression for the perimeter of the quadrilateral is 9a + 7.