The perimeter of a triangle is 74 cm. the longest side is 10 cm less than the sum of the other two sides. twice the shortest side is 2 cm less than the longest side. find the length of each side of the triangle shortest side : ? middle side : ? longest side : ?

Perimeter = 74cm

Let x be the shortest side
Let y be the middle side
Let z be the longest side

1) x + y + z = 74
2) z = x + y - 10
3) 2x = z - 2

From equation 1, we get
x + y = 74 - z

Substitute into equation 2.
z = (74 - z) - 10
z = 64 - z
2z = 64
z = 32

Substitute z = 32 into equation 3.
2x = 32 - 2
2x = 30
x = 15

Substitute x = 15 & z = 32 into equation 1.
15 + y + 32 = 74
y = 74 - 32 - 15
y = 27

Ithink it is 7. 16