# Make a letter expression to solve the problem: Length of the polyline KLMNP = 198cm.

**Make a letter expression to solve the problem: Length of the polyline KLMNP = 198cm. Link MN = 39 cm, which is 12 cm longer than KL. Link NP is by ,, c ,, cm longer than KL. Find the length of the LM link. Simplify the expression and calculate for ,, C ,, = 47**

Since we know the total length of the broken line KLMNP = 198 cm. It is also known that the broken line consists of segments: KL, LM, MN, NP.

So we get the following true equality:

KL + LM + MN + NP = 198.

We also know that MN = 39 cm and KL is 12 cm shorter.

Thus:

KL = MN – 12 = 39 – 12 = 27 cm.

Also from the condition we know that the NP link is c cm longer than KL, which means:

NP = KL + c = 27 + c.

Substitute all the values into the first expression and get the length of LM:

27 + LM + 39 + (27 + c) = 198;

LM = 198 – 27 – 39 – 27 – s;

LM = 105 – s;

We know that c = 47. Hence:

LM = 105 – 47 = 58 cm.

Answer: 58 cm.