Mathematics

Problem

\triangle LMN

, it is given that

\angle L = \angle M

. The sides opposite these angles are expressed as

LN = 3x - 5\,\text{cm}

and

MN = 2x + 7\,\text{cm}

. The third side

LM

measures

14\,\text{cm}

. Solve the following. a. (i) Determine the value of

x

. b. (ii) Hence, find the lengths of

LN

and

MN

. c. (iii) Calculate the perimeter of

\triangle LMN