Find the possible length of the three sides of two triangles whose perimeter is 21 cm

Perimeter =side+side+side 21cm=21/3=7cm

or -- 6,7,8

7

To find the possible lengths of the three sides of two triangles whose perimeter is 21 cm, we need to consider the conditions for triangle inequalities.

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.

Let's denote the lengths of the sides of the first triangle as a, b, and c, and the lengths of the sides of the second triangle as x, y, and z.

For the first triangle, we have the following inequality equations:
a + b > c
b + c > a
c + a > b

For the second triangle, we have the following inequality equations:
x + y > z
y + z > x
z + x > y

Since the perimeter of both triangles is 21 cm, we can set up the following equation:
a + b + c = x + y + z = 21

Now, let's analyze the possible values for a, b, and c.

We can start by assuming one side has the maximum possible length. Let's assume a = 10 cm as the maximum length a side can be. Now, we can use this assumption to calculate the possible values for b and c.

Using the inequality equations, we get:
10 + b > c
b + c > 10
c + 10 > b

We also know that a + b + c = 21, so substituting a = 10, we have:
10 + b + c = 21

From this equation, we can solve for b + c:
b + c = 21 - 10
b + c = 11

Now, we need to find the possible values of b and c, satisfying the inequality equations:
10 + b > c
b + c > 10
c + 10 > b
b + c = 11

We can try various combinations of values within these constraints, such as b = 5 and c = 6, or b = 4 and c = 7, and so on.

Repeat this process for different assumptions of maximum side lengths(a, x) to find other possible combinations for the first and second triangles.

Remember to consider values that satisfy the triangle inequality for both triangles.

By applying this approach, you will be able to find the possible lengths of the three sides of two triangles whose perimeter is 21 cm.