Q. 124.2( 5 Votes )

In an isosceles triangle ABC, if AB = AC = 13 cm and the altitude from A on BC is 5 cm, find BC.

Answer :

Given: isosceles triangle ABC, where AB = AC = 13 cm and the altitude from A on BC is 5 cm.

To find: The value of BC.

Solution:


In ADB


AD2+BD2=AB2


52+BD2=132


25+BD2=169


BD2=169-25


BD2=144


BD=


BD=12cm


In ADB and ADC


ADB=ADC =90


AB=AC=13cm


AD=AD (Common)


ADBADC (By RHS condition)


BD=CD=12cm (c.p.c.t)


As BC=BD+DC


BC=12+12


BC = 24cm

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