Question

In an equilateral triangle of side 3√3 cm, find the length of the altitude.
(Class 10 Maths Sample Question Paper)

Answer 1

SOLUTION:
Given:

Side of an equilateral ∆ABC= 3√3 cm.

AB= AC=BC = 3√3 cm

Let AD = h (Altitude)

BD = ½ BC( ALTITUDE BISECTS THE BASE)

BD= ½(3√3)= 3√3/2 cm

AB² = AD²+ BD²

(3√3)² = h² + (3√3/2)²

27 = h² + 27/4

h² = 27 - 27/4

h² = (27×4 -27)/4

h²= (108 -27)/4

h²= 81/4

h=√(81/4)

h= 9/2= 4.5 cm

h= 4.5 cm

Hence, the length of the altitude is 4.5 cm.

HOPE THIS WILL HELP YOU...

Answer 2

Answer:

Step-by-Side of equilateral triangle = 3√3

Altitude of equilateral triangle =  \frac{\sqrt{3}}2 a

=  \frac{\sqrt{3}}2 × 3√3

= (√3 × 3√3)/2

= 3(√3)²/2

= 3(3)/2

= 9/2

= 4.5

step explanation: