Answer :

Let the triangle be Δ ABC.

The triangle has two equal sides, i.e. AB = BC.


Let the length of the third side, ℓ (AC), be x meters. ℓ (AB) = ℓ (BC) = (2x – 5) meters.


The perimeter of Δ ABC = 55 meters.


According to the given condition,


ℓ (AB) + ℓ (BC) + ℓ (AC) = 55


2x – 5 + 2x – 5 + x = 55


5x – 10 = 55


5x = 55 + 10 (Transposing 10 to RHS)


5x = 65


x = (Transposing 5 to RHS)


x = 13


The lengths of the sides of the triangle are


ℓ (AB) = 2x – 5 = 2 (13) – 5 = 26 – 5 = 21 meters.


ℓ (BC) = 2x – 5 = 2 (13) – 5 = 26 – 5 = 21 meters.


ℓ (AC) = x = 13 meters.


The lengths of the sides of Δ ABC are 21 meters, 21 meters and 13 meters.


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