Question

The sides of a right angled triangle are in A.P. The ratio of sides is

• A. 1 : 2 : 3
• B. 2 : 3 : 4
• C. 3 : 4 : 5
• D. 5 : 8 : 3

Answer 1

The correct option is C 3 : 4 : 5

Let $a-d,a,a+d$ be the sides of Right angled triangles, which are in AP with first term $a$ and common difference $d$.
$\therefore (a+d{)}^2=a^2+(a-d{)}^2$ ($\because$ of right angled triangle.)
$\Rightarrow a^2+2ad+d^2=a^2+a^2-2ad+d^2$
$\Rightarrow a^2-4ad=0$
$\Rightarrow a(a-4d)=0$
$\Rightarrow a=0,4d$
But, $a=0$ is not possible.
Therefore, $a=4d$.
Hence side are $3d,4d,5d.$
i.e they are in ratio $3:4:5$
Option C is correct.