The areas of two similar triangles are 121 cm2 and 64 cm2 respectively. If the median of the first triangle is 12.1 cm, find the corresponding median of the other.

15.jpg


We have,


ABCPQR


Area () =121cm2


Area () =64cm2


AD= 12.1cm


AD and PS are the medians


By area of similar triangle theorem


Area() =AB2


Area () PQ2


AB2 =121


PQ2 64


AB =11 ………… (i)


PQ 8


ABCPQR


AB/PQ=BC/QR [Corresponding parts of similar triangles are proportional] AB/PQ=2BD/2QS [AD and BD are medians]


AB/PQ=BD/QS ………… (ii)


In ABD and PQS


B=Q [ABCPQS]


AB/PQ=BD/QS [from (ii)]


ABD ~ PQS [By AA similarity]


AB/PQ=AD/PS Compare equ. (i)and(ii)


AD/PS=11/8


12.1/PS=11/8


PS=12.1x8/8


PS= 8.8 cm


15