Question

If the area of an equilateral triangle is 18√3cmsqure .find its height

Answer 1

Area of an equilateral triangle = √3/4 a²

Where a² = square of the side

Also area would be 1/2 × a × h

Where h = height

So,

√3/4 a² = 18√3

=> a² = 18√3 ÷ √3/4

=> a² = 18√3 × 4/√3

=> a² = 18 × 4

=> a = √18 × √4

=> a = √9 × √2 × √4

=> a = 3 × 2√2

=> a = 6√2


Now area = 1/2 × a × h

=> 1/2 × a × h = 18√3

=> 1/2 × 6√2 × h = 18√3

=> 3√2 × h = 18√3

=> h = 18√3 × 1/3√2

=> h = 6√3/√2

=> h = 6√3/√2 ×√2/√2

=> h = 6√6/2

=> h = 3√6

Answer :- 3√6 cm

Answer 2

$\large \tt AHOY!! \:$


given area of the equilateral ∆ = 18√3cm²

formula for the area of an equilateral ∆ is √3/4s²

where 's' is the side of the equilateral ∆.

therefore √3/4 × s² = 18√3cm²

=> √3s² = 18√3 × 4

=> √3s² = 72√3cm²

=> s² = 72√3/√3

=> s² = 72cm²

=> s = √(2 × 2 × 2 × 3 × 3)

=> s = 12√2cm

hence the side of the equilateral triangle is 12√2cm

we all know the basic and the easiest formula for finding the area of a triangle. that is 1/2 × b × h

now we got the side 12√2cm. put 12√2 as base.

=> 1/2 × 12√2 × h = 18√3cm²

=> 6√2 × h = 18√3cm²

=> h = 18√3/6√2

=> h = 3√3/√2

by rationalizing we get,

=> h = 3√3/√2 × √2/√2

=> h = 3√6/2cm

hence the height of the ∆ is 3√6/2cm.

$\large \tt HOPE \: THIS \: HELPS!!$