Question

From a point in the interior of an equilateral triangle, the perpendiculars are drawn on the three sides. The

lengths of the perpendiculars are 21 cm, 15 cm and 9 cm. Find the perimeter and length of median of the

triangle.​

Answer 1

Answer:

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.

Thinking Process

(i) From a interior point a triangle, three triangle will be formed Determine area of each triangle by using the formula = 1/2 (Base x Height).

(ii) Determine the area of an equilateral triangle by using the Heron’s formula i.e.,

(iii) Further, equate the area of triangle by Heron’s formula and the sum of all three triangle. Simplify it to get the side of D. Hence, find area of the triangle.