Explanation:

- To solve this, we need to use the properties of a right-angled triangle.

- Let's denote the sides of the triangle as \(a\), \(b\), and the hypotenuse \(c\).

- From the given information:

- The perimeter formula is \(a + b + c = 36\).

- The area formula is \(\frac{1}{2} \times a \times b = 54\) which simplifies to \(a \times b = 108\).

- We already have two equations:

1. \(a + b + c = 36\)

2. \(a \times b = 108\)

- Rewriting the perimeter equation as \(a + b = 36 - c\).

- Use Pythagoras theorem: \(a^2 + b^2 = c^2\).

- These equations can be used to solve for \(c\).

- Option 3: 15 cm satisfies all equations.

- Correct Answer: Option 3

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