Question

What will be the length of the altitude of an equilateral triangle whose side is 9 cm?

(a) 4.567 cm

(b) 7.794 cm

(c) 8.765 cm

(d) 4.567 cm

I have been asked this question during an interview.

This interesting question is from Pythagoras Theorem in portion Triangles of Mathematics – Class 10

Answer 1

Right answer is (b) 7.794 cm

The best I can explain: Here, ABC is an equilateral triangle and AD is the altitude of the triangle.

Now, in ∆ADB

AB^2 = AD^2 + BD^2

9^2 = AD^2 + 4.5^2     (Since, AD is the altitude of the triangle it will bisect BC)

AD^2 = 81 – 20.25

AD^2 = 60.75

AD = √60.75 = \(\frac {9\sqrt {3}}{2}\) cm = 7.794 cm