Two equal sides of a triangle are each 5 metres less than twice the third side. If the perimeter of the triangle is 55 metres, find the lengths of its sides.

Let the length of the third side be x metres.

Then, each of the two equal sides = (2x - 5) metres.

Perimeter of the triangle = 55 metres.

We know the formula:

Perimeter of a triangle = Sum of all three sides

∴ 55 = (2x - 5) + (2x - 5) + x

⇒ 55 = 2x + 2x + x - 5 - 5

⇒ 55 = 5x - 10

⇒ 55 + 10 = 5x $\quad$ [Transposing -10 to LHS]

⇒ 65 = 5x

⇒ x = $\dfrac{65}{5}$

⇒ x = 13

∴ Third side = x = 13 m

Each equal side = (2x - 5) m = (2 x 13 - 5) m = (26 - 5) m= 21 m

Hence, the lengths of the sides of the triangle are 13 m, 21 m and 21 m.