Question

A square is drawn on the altitude of an equilateral triangle of side 2m

(i) What is the area of the square?

(ii) What is the altitude of the triangle?

(iii) What are the lengths of the other two sides of the triangle shown below?

Answer 1

(i)

BD = 1 m

AD = \(\sqrt{2^2-1^2}=\sqrt{4-1}=\sqrt{3}\)

Area of square

\(=\sqrt{3}\times\sqrt{3}\) = 3 sq. m

(ii) Height of triangle \(\sqrt{3}\) cm

(iii)

Sides are 1 m and \(\sqrt{3}\) m

Sides opposite to 30° angle = 1 m

Sides opposite to 60° = \(\sqrt{3}\) m