Question

ΔABC is an isosceles triangle with AB = AC = 13cm. The length of altitude from A on BC is 5cm. Find BC. 

Answer 1

It is given that Δ ABC is an isosceles triangle.
Also, AB = AC = 13 cm 

Suppose the altitude from A on BC meets BC at D. Therefore, D is the midpoint of BC.  

AD =5 cm
Δ 𝐴𝐷𝐵 𝑎𝑛𝑑 Δ 𝐴𝐷𝐶 are right-angled triangles.
Applying Pythagoras theorem, we have;  

  

`AB^2=AD^2+BD^2` 

`BD^2=AB^2-AD^2=13^2-5^2` 

`BD^2=169-25=144` 

`BD=sqrt144=12` 

Hence, 

`BC=2(BD)=2xx12=24 cm`