Question

Determine whether the triangle having sides ( a - 1 ) cm, $2\sqrt{a}$ cm and ( a + 1 ) cm is a right angled triangle.

Answer 1

$AB=(a-1)cm,BC=2\sqrt{a}cm,CA=(a+1)cm$

Hence, $A{B}^2=(a-1{)}^2=a^2+1-2a$

$B{C}^2=(2\sqrt{a}{)}^2=4a$

$A{C}^2=(a+1{)}^2=a^2+1+2a$

$A{B}^2+B{C}^2=a^2+1-2a+4a$

$A{B}^2+B{C}^2=a^2+1+2a$

$\therefore$ $A{C}^2=A{B}^2+B{C}^2$

So, $△ABC$ is a right-angled triangle.