Measurements taken in a triangle give (AD=24

MATHEMATICS · Single correct · GCSE · Mathematics · Number · Number

Problem

Measurements taken in a triangle give

AD=24\,\text{mm}

DB=32\,\text{mm}

AE=21\,\text{mm}

and

EC=28\,\text{mm}

, each correct to the nearest millimetre (possible error

\pm1\,\text{mm}

on each length). What can be concluded about

DE

being parallel to

BC

? (a)

DE

is certainly parallel to

BC

for all possible true lengths. (b)

DE

can never be parallel to

BC

for any combination of true lengths within the error limits. (c) Depending on the actual values within the error range,

DE

may or may not be parallel to

BC

. (Correct) (d)

DE

will be parallel to

BC

only if the absolute errors in

AD

and

AE

are equal.