1.

The area of an equilateral triangle is 81root3.Find its height ​

Answer»

GIVEN:-

To Find:-

  • Height of the triangle

FORMULA Used:-

  • Area of equilateral triangle = (√3/4) × (Side)²

  • Area of triangle = ½ × Base × Height

Solution:-

▪︎Finding side of triangle

According to given conditions;

Area of equilateral triangle = 81√3 cm²

➟ (√3/4) × (Side)² = 81√3 cm²

➟ √3 × (side)² = 81√3 × 4

➟ (Side)² = 324√3 ÷ √3

➟ Side = √324

∴ Side = 18cm

▪︎Finding Height of triangle

As we know,

Area of triangle = ½ × base × height

Here,

Base = Side = 18 cm

According to given conditions;

Area of triangle = 81√3 cm²

➟ ½ × base × Height = 81√3 cm²

➟ ½ × 18 × Height = 81√3 cm²

➟ 9 × Height = 81√3 cm²

➟ Height = 81√3 cm² ÷ 9

∴ Height = 9√3 cm


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