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Question
An isosceles triangle has equal sides each 13 cm and a base 24 cm in length. Find its height
Solution
In an isosceles triangle the altitude dives its base into two equal parts.
Now in the figure, ∆ABC is an isosceles triangle with AD as its height
In the figure, AD is the altitude and ∆ABD is a right triangle.
By Pythagoras theorem,
AB2 = AD2 + BD2
⇒ AD2 = AB2 – BD2
= 132 – 122 = 169 – 144 = 25
AD2 = 25 = 52
Height: AD = 5 cm
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