The sides of a right-angled triangle containing the right angle are (5x) cm and (3x - 1) cm. If its area is 60 cm², find its perimeter.

Let ABC be a right-angled triangle,

AB = 5x cm and BC = (3x – 1) cm

We know that,

Area of △ ABC = $\dfrac{1}{2}$ × base × height

Substituting the values we get,

⇒ 60 = $\dfrac{1}{2}$ × (3x - 1) × 5x

⇒ 120 = 5x(3x – 1)

⇒ 120 = 15x² - 5x

⇒ 15x² - 5x - 120 = 0

⇒ 5(3x² - x - 24) = 0

⇒ 3x² - x - 24 = 0

⇒ 3x² – 9x + 8x – 24 = 0

⇒ 3x(x – 3) + 8(x - 3) = 0

⇒ (3x + 8)(x - 3) = 0

⇒ 3x + 8 = 0 or x - 3 = 0

⇒ 3x = -8 or x = 3

⇒ x = $\dfrac{-8}{3}$ or x = 3.

Since, x cannot be negative. So, x = 3.

⇒ AB = 5 × 3 = 15 cm

⇒ BC = (3 × 3 – 1) = 9 – 1 = 8 cm

In right angled △ABC,

Using Pythagoras theorem,

AC² = AB² + BC²

Substituting the values we get,

⇒ AC² = 15² + 8²

⇒ AC² = 225 + 64

⇒ AC² = 289

⇒ AC = $\sqrt{289}$

⇒ AC = 17 cm.

Perimeter of a triangle = Sum of all the sides of a triangle

= AB + BC + AC

= 15 + 8 + 17

= 40 cm.

Hence, perimeter of the triangle = 40 cm.