The parameter of a triangle is 4 cm. The one side is 7 cm longer than the other and 5 cm shorter than the third . Find length of each side of the triangle

Answer 1

Let's call the lengths of the sides of the triangle x, x+7, and x+5.

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

So we can set up the following inequalities:

x + (x+7) > x+5
2x + 7 > x + 5
x > -2

x + (x+5) > x+7
2x + 5 > x + 7
x > 2

x+5 + (x+7) > x
2x + 12 > x
x > -12

Since x > -2 and x > -12, the smallest possible value for x is 2.

So the lengths of the sides of the triangle are 2 cm, 9 cm, and 7 cm respectively.