The three perpendicular distance of three sides of an equilateral triangle from a point which ...........

Quantitative Aptitude ( CCS) Mensuration 2D

The three perpendicular distance of three sides of an equilateral triangle from a point which lies inside that triangle are 6 cm, 9 cm, and 12 cm, respectively. The perimeter of the triangle is

42√2 cm

45√3 cm

52√2 cm

54√3 cm

छोटे Courses बड़े Results

Master Mensuration 2D

Prepare through Micro-courses

Try Now

Explanation:

let O be the point inside the equilateral triangle ABC of side ‘a’ cm.
Let OR = 12 cm , OQ = 9 cm and AR = 6 cm
Then,
Area of triangle ABC = Area of triangle BOC + Area of triangle AOC + Area of triangle AOB
√3/4 a^2= 1/2 BC×OR+1/2 AC ×OQ+1/2 AB× OP
√3/4 a^2 = 1/2× a × 12 + 1/2×a ×9+1/2×a× 6
√3/4 a^2 = a (12/2+ 9/2+ 6/2)
√3/4 a = ((12+9+6)/2)
a = 4/√3 × 27/2
a = 54/√3 cm
∴ Perimeter = 3 × a = 3 × 54/√3 = 54√3 cm