In a right-angled triangle, if sum of the squares of the sides making right angle is 169

Explanation:- 

The given information can be written in the form of the Pythagorean theorem which states that in a right-angled triangle, the sum of the squares of the two shorter sides (adjacent and opposite to the right angle) is equal to the square of the longest side (the hypotenuse). Mathematically, it can be represented as: [a^2 + b^2 = c^2] where ‘a’ and ‘b’ are the shorter sides and ‘c’ is the hypotenuse of the right-angled triangle.

In the given question, it is given that the sum of the squares of the sides making right angle is 169. Let’s assume that ‘a’ and ‘b’ are the shorter sides, then we can write it as: [a^2 + b^2 = 169] Now, we need to find the length of the hypotenuse ‘c’. Since ‘c’ is the longest side, it will be the square root of the sum of the squares of the other two sides. Mathematically, it can be represented as: [c = \sqrt{a^2 + b^2}]

So, we need to find the square root of 169 to get the length of the hypotenuse. We know that 169 can be written as 13^2. Therefore, the length of the hypotenuse ‘c’ is 13.

Hence, the correct answer is option (b) 13.