Mathematics

Mathematics

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}

. a. (i) Show that

\triangle LMN \sim \triangle OPQ

. b. (ii) Find the value of

x

. c. (iii) Determine the scale factor from

\triangle LMN

to

\triangle OPQ

. d. (iv) Calculate the length

MN

.

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