Find the sides of a triangle whose perimeter is 27 cm, if one of them is 5 cm larger than the second and 1 cm larger than the third.

Given:

Triangle with sides a, b and c

P = 27 cm

b> a by 5 cm

b> c by 1 cm

The expression for finding the parties:

b = a + 5;

b = c + 1;

Consequently:

a = b – 5 and c = b -1.

Formula for finding the perimeter P = a + b + c:

P = b + (b – 5) + (b – 1);

P = b + b – 5 + b -1;

P = 3b – 6;

3 (b – 2) = 27;

b – 2 = 27: 3;

b – 2 = 9;

b = 9 + 2;

b = 11 cm.

Find side a:

a = b – 5;

a = 11 – 5;

a = 6 cm.

Find side c:

c = b – 1;

c = 11 – 1;

c = 10 cm.

Answer: a = 6 cm, b = 11 cm, c = 10 cm (1, 3, 6)