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An isosceles triangle has equal sides each 13 cm and a base 24 cm in length. Find its height

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#### 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,

AB^{2} = AD^{2} + BD^{2}

⇒ AD^{2} = AB^{2} – BD^{2}

= 13^{2} – 12^{2} = 169 – 144 = 25

AD^{2} = 25 = 5^{2}

**Height:** AD = 5 cm

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