Question

find the perimeter of an equilateral triangle whose area is equal to that of a triangle with side is 21 cm 16 cm 13 cm answer correct to 2 decimal places

Answer 1

Answer:

46.48 cm

Step-by-step explanation:

Use Heron's Formula to get the area of the triangle.

semiperimeter s = ( 21 + 16 + 13 ) / 2 = 25

area = √[ s(s-a)(s-b)(s-c) ]

      = √[ 25 × (25-21) × (25-16) × (25-13) ]

      = √[ 25 × 4 × 9 × 12 ]

      = 5 × 2 × 3 × 2√3

      = 60√3.

Let a be the side of the equilateral triangle and h its height.

Then by Pythagoras' Theorem applied to half of the triangle (or use trigonometry: sin 60° = h / a), we get

h = a√3 / 2

So the area is

(1/2) × a × h = 60√3

=> (1/2) × a × a√3/2 = 60√3

=> a² = 60 × 4 = 240

=> a = 4√15

=> perimeter = 3a = 12√15

=> perimeter ≈ 46.48   (to 2 decimal places)