Question

what is the ratio sides of the triangle

• A. 1 : √2 : √3
• B. 2 : 3 : 1
• C. √2 : 2 : √3 + 1
• D. √3 : 1 : √2

Answer 1

Answer:

C. √2 : 2 : √3 + 1

Cut triangle ABC into 2 by drawing a perpendicular through angle ACB

So we get two triangles ABD with angles 30° 60° 90° and triangle BDC with angles 45° 45° 90°

We know that,

ratio of sides of a triangle with angles 45°, 45°, 90° is 1 : 1 : √2

and, ratio of sides of triangle with angle 30, 60, 90 is = 1 : √3 : 2

So the ratio of sides triangle ABC is √2 : 2 : √3 + 1