The sides of a right triangle containing the right angle are (5x) cm and (3x - 1) cm. If the area of the triangle be 60 cm, calculate the length of the sides of the triangle.

Answer: hypotenuse (h) = 17 cm

The area of a right triangle is found using the formula 1/2 x base x height.

Using the provided information the equation becomes:

60 = 1/2 * 5x * (3x-1)

Combine 1/2 and 5x:

60 = 5x/2 * (3x-1)

Multiply each term by 2/5:

24 = 3x^2 - x

Subtract 24 from each side:

3x^2 - x - 24 = 0

Now factor the polynomial:

(x-3) (3x+8) = 0

Solve for each x for 0:

3-3 = 0, so x = 3

3x + 8 = 0 : subtract 8 from each side:

3x = - 8

divide both sides by 3: x = - 8/3

Since a side of a triangle cannot be a negative value, we now know x = 3

Now replace x in each side with 3 and solve:

5x = 5 (3) = 5 x 3 = 15

3x-1 = 3 (3) - 1 = 9-1 = 8