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ABC is an equilateral triangle of side 2a. Find each of its altitudes. - Mathematics

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ABC is an equilateral triangle of side 2a. Find each of its altitudes.

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Solution

Let AD be the altitude in the given equilateral triangle, ΔABC.

We know that altitude bisects the opposite side.

∴ BD = DC = a

In ΔADB

∠ADB = 90º

Applying pythagoras theorem we obtain

AD2 + DB2 = AD2

⇒ AD2 + a2 = (2a)2

⇒ AD2 + a2 = 4a2

⇒ AD2 = 3a2

⇒ AD =`asqrt3`

In an equilateral triangle, all the altitudes are equal in length. Therefore, the length of each altitude will be `sqrt3a`

Concept: Right-angled Triangles and Pythagoras Property
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APPEARS IN

NCERT Class 10 Maths
Chapter 6 Triangles
Exercise 6.5 | Q 6 | Page 150

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