Question

In triangle abc, p and q are the mid points of the sides ab and ac respectively. r is a point on the segment pq such that pr : rq is 1 : 2 if pr = 2 cm. find the length of bc.

Answer 1

In triangle ABC , P and Q are the mid points of the sides AB and AC respectively.

R is a point on the segment PQ such that

PR : RQ is 1 : 2

PR = 2 cm.

$\red { To \: find : } \\Length \: of \: BC .$

$\underline { Solution :}$

$i ) PR : RQ = 1 : 2 \: (given)$

$\implies RQ = 2PR \\\implies RQ = 2 \times 2 \:cm \: ( given )$

$\implies RQ = 4 \:cm$

$ii ) PQ = PR + RQ$

$\implies PQ = 2 \:cm + 4 \:cm = 6\:cm$

$iii ) Now, Length \:of \: BC = 2\times PQ$

$\pink {( The \:line \: segment \: joining \:the }\\\pink { mid-points \:of \:two \:sides \:of \:a }\\\pink { triangle\: is \: parallel \:to \:the \:third \:side \: and}\\\pink { and \:also \:half \:of \:it )}$

$= 2 \times 6 \:cm \\= 12 \:cm$

Therefore.,

$\red {Length \:of \: BC}\green {= 12 \:cm }$

•••♪