Question

if the area of an equilateral triangle is 8 root 3 cm square find its height

Answer 1

solution.

Area of equilateral trangle= root3/4 (side)^2

ATQ,

=> root3/4 (side)^2= 8 root3

=> (side)^2= 32

=> Side= root 32 or 4√2

Now, we know that altitude [Height] busect the opposite side .

we know that area of traingle = 1/2* Base* Height

=> 8√3 = 1/2 * 4√2 *height

=> 8√3 = 2√2 * height

=> height = 2√6 cm
___________

hope it helps you☺☺

Answer 2

$Heya$‼

Area of an equilateral ∆ = 8√3 cm²
√3a² / 4 = 8√3
a² = ( 8√3 × 4 ) / √3
a² = 8 × 4
a² = 32
a = √32
a = 4√2 cm

Area of ∆ = 1 / 2 × base × height
8√3 = 1 / 2 × 4√2 × height
height = ( 2 × 8 √3 ) / 4√2
=> 16√3 / 4√2
=> 4√3 / √2
=> 4√3 / √2 × √2 / √2
=> 4√6 / 2
=> 2√6 cm

Therefore, height of the equilateral ∆ is 2√6 cm.