Question

if the area of an equilatral triangle is 50 root 3cm² then find the length of its altitude​

Answer 1

Answer:

Height is 5√6 cm

Step-by-step explanation:

Area of equilateral Triangle = √3/4 x s²

Let side of equilateral triangle x

50√3 = √3/4 x (x)²

x² = 50√3 x 4

          √3

x² = 200

x = √200

x = 10√2 cm

In an equilateral triangle ,

Height = √3/2 x s

Let height be h. Since x = 10√2 cm

h = √3/2 x 10√2

h = 10 √6 / 2

h = 5√6 cm

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Answer 2

Given :   area of an equilateral triangle is 50√3

To Find :  the length of its altitude​

Solution:

area of an equilateral triangle  =(√3 / 4)  (side)²

(√3 / 4)  (side)² = 50√3

=> (side)²  = 200

=> side = 10√2  

Area of triangle = (1/2) * base * altitude​

=> (1/2) *  10√2    * altitude​ = 50√3

=>  altitude​ = 10√3/√2

length of its altitude​ = 10√3/√2  units

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