Question

the construction of triangle LMN in which LM=8 cm , angle L=45 is possible when (MN+LN) is​

Answer 1

The construction of triangle LMN,$MN+NL> 8 cm$.

Step-by-step explanation:

1. Let $NL< MN<LM$    ...1)

  where in triangle LMN

  smallest side = NL

  Largest side = LM

2. Construction of triangle is only possible  

    When sum of two smaller side is greater than largest side of triangle.

   Means

  $NL+MN > LM$       ...2)

3. Equation 2) can also be written as

   $NL > LM-MN$       ...3)

4. On focus on equation 3), we can say that size of smallest side of triangle is greater than difference of other two side.

5. Criteria of Triangle

   a.  When sum of two smaller side is greater than largest side of triangle.

  b.  size of smallest side of triangle is greater than difference of other

        two side.

Answer 2

Hope this is helpful for you.