A civil engineer is marking points on two sides of a triangular plot so that the…

MATHEMATICS · Subjective · CBSE · Mathematics · Triangles · Triangles

Problem

A civil engineer is marking points on two sides of a triangular plot

PQR

so that the joining line becomes parallel to the third side. She intends to mark point

S

PQ

and point

T

PR

such that

ST\parallel QR

. Her measuring tape, however, has a possible error of

\pm0.1\text{ cm}

. The intended measurements are:

PS=7.0\text{ cm}

SQ=5.0\text{ cm}

PT=8.4\text{ cm}

and

TR=6.0\text{ cm}

. (i) Verify, without considering the measuring error, whether these lengths satisfy the required condition for

ST

to be parallel to

QR

. (ii) Taking measurement errors into account, find the maximum and minimum possible ratios

\dfrac{PS}{SQ}

and

\dfrac{PT}{TR}

. (iii) Decide, with clear reasoning, whether

ST

will certainly, possibly, or certainly not be parallel to

QR

in the worst-case scenario of measurement errors.