Question

The area of an equilateral triangle is numerically equal to its perimeter find its perimeter correct to 2decimal places

Answer 1

Given,

Area of ∆ABC = Perimeter of ∆ABC

(numerically)

Height = AD = √(AC² - DC²)

(Pythagoras theorem)

= √(a² - a²/4) = √3a/2

Area = 1/2 × base × height

= 1/2 × a × √3a/2 = √3a²/4

Perimeter = AB + BC + CA

= a + a + a = 3a

⟹ √3a²/4 = 3a

⟹ a/4 = √3

⟹ a = 4√3

∴ Perimeter = 3(4√3)

= 12√3

= 12 × 1.73

= 20.76 cm