Mathematics

Problem

A footbridge is supported on each bank of a canal by identical triangular frames. On the left bank, a vertical post

PQ

of height

3\,\text{m}

is fixed to the ground at

Q

, and a slant beam

PR

of length

5\,\text{m}

is connected from the top

P

of the post to a point

R

on the bank such that

QR

is horizontal. On the right bank, a similar arrangement is made with a vertical post

ST

of height

3\,\text{m}

and a slant beam

SU

of length

5\,\text{m}

touching the ground at

U

so that

TU

is horizontal. a. Prove that the two triangular frames

\triangle PQR

and

\triangle STU

are congruent. b. Find the lengths of

QR

and

TU

. c. Calculate the combined length of the two horizontal members

QR + TU