Find the in-radius (in cm) of an equilateral triangle whose sides are 6cm each.
- A3
- B2
3
- C3
3
- D4
3
Solution & Step-by-step Explanation
The formula for the in-radius (r) of an equilateral triangle with side length a is given by:
r=
2
3
a
Given that the side of the equilateral triangle is a=6cm:
r=
2
3
6
r=
3
3
Rationalizing the denominator:
r=
3
×
3
3×
3
=
3
3
3
=
3
cm
r=
2
3
a
Given that the side of the equilateral triangle is a=6cm:
r=
2
3
6
r=
3
3
Rationalizing the denominator:
r=
3
×
3
3×
3
=
3
3
3
=
3
cm