a, b and c are the integral sides of a right angled triangle in which c is the hypotenuse measuring `3sqrt5` metres. If side 'a' is increased by `(400)/(3)%` and side 'b' is increased by
`(50)/(3)%`, then their total becomes 14 metres. Find the area of triangle.

Explanation

To solve the problem step by step, we will follow the logical sequence outlined in the video transcript.

### Step 1: Identify the given information
We have a right-angled triangle with integral sides \( a \), \( b \), and \( c \) (the hypotenuse). The hypotenuse \( c \) is given as \( 3\sqrt{5} \) meters.

### Step 2: Use the Pythagorean theorem
According to the Pythagorean theorem:
\[
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