Question

The construction of a triangle LMN in which LM=8cm,angle L=45* is possible when (MN+LN) is ___cm.

Answer 1

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

Step-by-step explanation:

1. Let NL< MN

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 > LMNL+MN>LM ...2)

3. Equation 2) can also be written as

NL > LM-MNNL>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.

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