Q12 of 168 Page 4

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

12.jpg


In ADB


AD2+BD2=AB2


52+BD2=132


25+BD2=169


BD2=169-25


BD2=144


BD=


BD=12cm


In ADB and In ADC


∠ADB=∠ADC =90


AB=AC=13cm


AD=AD (Common)


ADB≅ADC (By RHS condition)


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


BC=BD+DC


BC=12+12


BC=24cm


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