Question

Determine whether the triangle having sides (a − 1) cm, 2√a cm and (a + 1) cm is a right angled triangle.

Answer 1

SOLUTION :  

Given : Triangle having sides (a - 1) cm, 2√a and (a + 1) cm.  

Let ABC be the triangle in which with the sides are  AB = (a - 1)cm ,  BC = (2√ a) cm, CA = (a + 1) cm  

Hence, AB² = (a -1)²  = a² + 1² -2×a×1  

[(a- b)² = a²+b² - 2ab]

AB² = a² + 1 -2a

BC² = (2√ a)²

BC = 4a

CA² = (a + 1)²  = a² + 1² + 2×a×1  

[(a + b)² = a²+b² + 2ab]

CA² = a² + 1 + 2a

AC² = AB² + BC²

[By pythagoras theorem]

a² + 1 + 2a = a² + 1 - 2a + 4a

a² + 1 + 2a = a² + 1 + 2a

Hence, AC² = AB² + BC²

This proves that ∆ABC is right angled ∆ at B.

HOPE THIS ANSWER WILL HELP YOU

Answer 2

Solution explained below.

Let ABC be a triangle with AB= (a-1) cm, BC= 2√a cm and CA= (a+1) cm.

Therefore, AB^2= (a-1)^2
=a^2+1-2a

BC^2= (2√a)^2
=4a

CA^2= (a+1)^2
=a^2+1+2a

•°• AB^2+BC^2=AC^2

From the above solution it is proved that triangle ABC is right angled at B which means it is a right angled triangle.

Comment below if any doubt occurs.