From a point in the interior of an equilateral triangle, perpendicular

1.	From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.
Answer» According to the question, The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. We know that, Area of an equilateral triangle of side a = √3/4 a² We divide the triangle into three triangles, Area of triangle = (1/2 × a × 14) + (1/2 × a × 10) + (1/2 × a × 6) √3/4 a² = ½ × a × (14 + 10 + 6) √3/4 a² = ½ × a × 30 a = 60/√3 = 20√3 Area of the triangle = √3/4 a² =√3/4 (20√3)² = 300√3 cm²

From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.

Answer»

According to the question,

The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm.

We know that,

Area of an equilateral triangle of side a = √3/4 a²

We divide the triangle into three triangles,

Area of triangle = (1/2 × a × 14) + (1/2 × a × 10) + (1/2 × a × 6)

√3/4 a² = ½ × a × (14 + 10 + 6)

√3/4 a² = ½ × a × 30

a = 60/√3

= 20√3

Area of the triangle = √3/4 a²

=√3/4 (20√3)²

= 300√3 cm²