Let a and b denote llie lengths of the legs of a right triangle with following properties:
(i) All three sides of the triangle are integers.
(ii) The perimeter of the triangle is numerically equal to its area.
(iii) a ltb.
Statement-1: The number of such triangle is 2
Statement-2: Maximum possible perimeter of the triangle is 30°.

Options

A. Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement- 2 is True.

Explanation

To solve the problem, we need to find integer right triangles (Pythagorean triplets) that satisfy the conditions given in the question. Let's break down the solution step by step:

### Step 1: Understand the Properties of the Triangle
We have a right triangle with legs \( a \) and \( b \) (where \( a < b \)), and the hypotenuse \( c \). The properties we need to satisfy are:
1. All sides are integers.
2. The perimeter is equal to the area.
3. \( a < b \).

...