Find the altitude of an equilateral triangle of side 8 cm.

Options

A. `5sqrt3`
B. `3sqrt3`
C. `4sqrt3`
D. `2sqrt3`

Answer

C

Explanation

Let ABC be an equilateral triangle of side 8 cm. i.e, AB=BC=CA=8 cm.
Draw altitude AD which is perpendicular to BC. Then, D is the mid-point of BC.
`thereforeBD=CD=1/2BC=8/2=4cm`
Now, `AB^(2)=AD^(2)+BD^(2)` [by Pythagoras theorem]
`rArr (8)^(2)=AF^(2)+(4)^(2)`
`rArr 64=AD^(2)+16`
`rArrAD^(2)=64-16=48`
`rArr AD=sqrt48=4sqrt3`
Hence, altitude of an equileteral triangle is `4sqrt3` cm