Question

The points A(0, 0), B(10, 0), C(5, 5√3 ) are the vertices of the triangle ABC. Find AB, BC, AC and prove that the triangle is equilateral.

Answer 1

A(0, 0), B(10, 0), C (5, 5√3)

AB = 10 unit

BC = \(\sqrt{(10-5)^2+(0-5\sqrt{3})^2}\)

= \(\sqrt{25+75}\) = 10 unit

AC = \(\sqrt{(10-5)^2+(0-5\sqrt{3})^2}\)

= \(\sqrt{25+75}\) = 10 unit

AB = BC = AC

∴ ΔABC is equilateral