Final answer:
To find the length of diagonal CM in parallelogram NCSM, we use the properties of a parallelogram's diagonals bisecting each other and set up equations based on the given lengths to solve for a and b.
Step-by-step explanation:
The question asks us to find the length of diagonal CM in parallelogram NCSM. Since the diagonals NS and MC intersect at point P, they bisect each other in a parallelogram. First, we express the lengths given in terms of a and b:
- NP = 4a + 20
- NS = 13a
- PC = a + b
- PM = 2b - 2
Knowing that NP + PS = NS and PM + PC = MC, we can write:
- 4a + 20 + PS = 13a (since NP + PS = NS)
- 2b - 2 + a + b = MC (since PM + PC = MC)
To find PS, we rearrange the first equation:
PS = 13a - (4a + 20) = 9a - 20
Since PS = PC (diagonals bisect each other), we now have:
9a - 20 = a + b
This allows us to find the relationship between a and b. After solving these equations, we use the second relationship (PM + PC = MC) to find CM.