Question

The three sides of a right triangle have integral lengths, which form an arithmetic progression. Choose one of the possible lengths from the given options.

• A. $22$
• B. $58$
• C. $81$
• D. $361$

Answer 1

The correct option is C $81$

Let the sides be $(a-d),a,(a+d)$

Given: $\Delta$ is right-angled

$\therefore (a-d{)}^2+a^2=(a+d{)}^2$

$\Rightarrow a^2-2ad+d^2+a^2=a^2+2ad+d^2$

$\Rightarrow a^2=4ad$

$\therefore a=4d$

$\therefore Sides=3d,4d,5d$

$\therefore$ Given options should be divisible by 3 or 4 or 5

81 divisible by 3.

$(Ans\to C)$