Question

If the sides of a right angled traingle are in A.P., then the sides are proportional to.

• A. 1: 2: 3
• B. 2: 3: 4
• C. 3: 4: 5
• D. 4: 5: 6

Answer 1

Answer: (C)

3: 4: 5

Answer 2

Let the sides of the triangle be $a - d , a , a + d$ , then hypotenuse being the greatest side $a + d$.

So, $( a + d ) ^ { 2 } = a ^ { 2 } + ( a - d ) ^ { 2 }$

$\Rightarrow a ^ { 2 } + d ^ { 2 } + 2 a d = a ^ { 2 } + a ^ { 2 } - 2 a d + d ^ { 2 } \Rightarrow a = 4 d$

Therefore ratio of the side

$s = a - d : a : a + d$

$= ( 4 d - d ) : 4 d : ( 4 d + d ) = 3 : 4 : 5$.