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
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.
Let's assume the lengths of the sides of the triangle are x cm, (x + 7) cm, and (x - 5) cm.
According to the problem, the perimeter of the triangle is 4 cm. The perimeter of a triangle is the sum of the lengths of all its sides.
So, we can set up the following equation to find x:
x + (x + 7) + (x - 5) = 4
Simplifying the equation, we get:
3x + 2 = 4
Subtracting 2 from both sides, we have:
3x = 2
Dividing both sides by 3, we obtain:
x = 2/3
Now, we can find the lengths of the sides of the triangle:
First side: x cm = (2/3) cm
Second side: (x + 7) cm = (2/3 + 7) cm = (2/3 + 21/3) cm = 23/3 cm
Third side: (x - 5) cm = (2/3 - 5) cm = (2/3 - 15/3) cm = -13/3 cm (Note: The length of this side is negative, which is not possible for a triangle. Therefore, there is no valid solution for this problem.)
Hence, we can see that there is no valid solution for the lengths of the sides of the triangle.