Question

In the figure above, a circle is tangent to the side of equilateral ∆ PQR and the radius is 5. What is the perimeter of the ∆ PQR?

Answer 1

hint -
the altitude of triangle = 15 (why ?)

Answer 2

because 1/3 of 15 is 5?

Answer 3

yea thats right the exact reason is, since it is an equilateral triangle, the median and altitude overlap

Answer 4

so incenter and centroid lie at same location - at the center of circle

Answer 5

so we can use the median property which says, the centroid cuts the median in 2:1 ratio.

thats how we get altitude = 15

Answer 6

oh ok thank you i didn't know the actual reason behind that lol

Answer 7

its okay :) hope u get it nw.. .

now you knw the height of triangle, what u need to find perimeter ?

Answer 8

I get it :D answer is C because it's a 30-60-90 triangle. thank you!

Answer 9

np yw :))