Question

Find the perimeter of an equilateral triangle whose area is equal to that of a triangle with sides 21 cm and 13 cm and 16 centimetre

Answer 1

Answer:

refer to the attachment

Answer 2

Answer:

area of equilateral ∆le = area of other ∆le

(√3/4)A² = √[s(s-a)(s-b)(s-c)]

A = side of eq. ∆le

s = semiperimeter of other triangle

a, b, c = sides of other triangle

a = 21

b = 13

c = 16

s = (21 + 13 + 16)/2 = 50/2 = 25

So,

(√3/4)A² = √[25(25-21)(25-13)(24-16)]

= √[25(4)(12)(9)] = 60√3

=> A² = (60√3)(4/√3) = 240

A = √240 = 4√15

Perimeter = 3A = 12√15 cm