Problem

Problem

In

\triangle ABC

, let

AD

be the median to side

BC

. In

\triangle PQR

, let

PS

be the median to side

QR

. It is given that

AD = 9\,\text{cm}

,

PS = 6\,\text{cm}

and

BC = 15\,\text{cm}

. Further,

\angle A = \angle P

and

\angle C = \angle R

. a. (a) Prove that

\triangle ABC \sim \triangle PQR

. b. (b) Using part (a), calculate the length of

QR

. c. (c) If

AB = 13\,\text{cm}

, determine

PQ

. d. (d) Find the ratio

[\triangle ABC] : [\triangle PQR]

.

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