Q19 of 56 Page 6

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

Given: AB = AC = 13 cm


AD = 5 cm


To find: The length of BC.


Theorem Used:


Pythagoras theorem:


In a right-angled triangle, the squares of the hypotenuse is equal to the sum of the squares of the other two sides.


Explanation:



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)


∆ADB ≅∆ADC (By RHS condition)


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


BC=BD+DC


BC=12+12


BC=24cm


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