Question

The sides of certain triangles are given below. Determine which of them are right triangles. 

(a – 1) cm, `2sqrta` cm, (a + 1) cm

Answer 1

P = (a-1) cm, q = `2sqrta` 𝑐𝑚 𝑎𝑛𝑑 𝑟=(𝑎+1)𝑐𝑚
Then, 

`p^2+q^2=(0a-1)^2+(2sqrta)^2`  

=`a^2+1-2a+4a` 

=`a^2+1+2a` 

=`(a+1)^2` 

`r^2=(a+1)^2` 

`p^2+q^2=r^2` 

Thus, the given triangle is right-angled.