The perimeter of a triangle is 19 cm. if the length of the longest side is twice that of the shortest side and 3 cm less than the sum of the lengths of the other two sides, find the length of the three sides.

x - length of the shortest side

2x - length of the longest side

y - length of the third side

1) Longest side(2x) is "3 cm less than the sum of the lengths of the other two sides(x+y)" :

2x= x+y - 3 → x - y = - 3

2) "The perimeter of a triangle is 19 cm."

x + 2x + y = 19 → 3x + y = 19

3) We have a system of equations now.

x-y = -3

3x+y= 19

We can add these equations:

x-y+3x+y = -3 +19

4x = 16

x=4 (cm) is a shortest side.

2x = 2*4 = 8 (cm) is a longest side.

3x + y = 19 → 3*4 +y = 19 → 12 + y = 19 → y = 7 (cm) is a third side of the triangle.

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation: