A, B, C are three points such that AB = √50 cm, BC = √98 cm, AC = √288 cm. Do they lie on a straight line?

Question

A, B, C are three points such that AB = \(\sqrt{50}\) cm, BC = \(\sqrt{98}\) cm, AC = \(\sqrt{288}\) cm. Do they lie on a straight line?

Answer 1

If A, B, C are points on the same line then AB + BC = AC

AB + BC = \(\sqrt{50}+\sqrt{98}\)

\(=\sqrt{25\times2}+\sqrt{49\times2}\)

\(=5\sqrt{2}+7\sqrt{2}=12\sqrt{2}\) cm

AC = \(\sqrt{288}=\sqrt{144\times2}\)

= \(12\sqrt{2}\) cm

Here AB + BC = AC. So the three given points are on the same straight line.