Question

in an equilateral triangle, h-r=15, where h is height and r is circumradius then what is area of triangle​

Answer 1

Answer:

In an equilateral triangle, if H-R=15cm where H=height of the triangle & R= circumradius, then what is the area of triangle?

We know that in the case of an equilateral triangle the circumcentre,in centre, orthocentre and the centroid are one and the same.

Also centroid will divide the median in the ratio 2:1. If ABC is an equilateral triangle and if AD is the median then the circumcentre O will lie on ADsuch that AO:OD= 2:1. If AO=2x, then OD=x

That is H= 3x, R=2x => 3x-2x=15 => x =15

So H = 3×15=45 cm

But height of the equilateral triangle = (√3/2)a

So (√3/2)a = 45 => a = 45×2/√3=90/√3=30√3 cm.

So area of the equilateral triangle = (√3/4)a^2

=(√3/4)(30√3)(30√3)=675√3 sq.cm