Two triangles and are drawn such that

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

Two triangles

LMN

and

OPQ

are drawn such that

\angle L = \angle O

. Their side measurements are

LM = 3x + 1

LN = 5x + 3

OP = 8\,\text{cm}

and

OQ = 14\,\text{cm}

. It is further known that

PQ = 10\,\text{cm}

. (i) Show that

\triangle LMN \sim \triangle OPQ

. (ii) Find the value of

x

. (iii) Determine the scale factor from

\triangle LMN

\triangle OPQ

. (iv) Calculate the length

MN