find possible lengthsof three sides of two triangles whose perimeter is 21 cm
7,7,7 and http://math.stackexchange.com/questions/785764/given-perimeter-of-triangle-and-one-side-find-other-two-sides
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To find the possible lengths of three sides of two triangles with a perimeter of 21 cm, we need to consider the triangle inequality theorem. According to this theorem, the sum of any two sides of a triangle must be greater than the third side.
Let's denote the three sides of the triangle as A, B, and C. The perimeter is given as 21 cm, so we have:
A + B + C = 21 cm
Now, let's go through the possible combinations of values for the three sides and check if they satisfy the triangle inequality theorem.
1. A = 1 cm:
In this case, B + C = 21 - 1 = 20 cm. We need to find pairs of values (B, C) that satisfy the inequality theorem.
Possible combinations: (10 cm, 10 cm), (9 cm, 11 cm), (8 cm, 12 cm), ..., (1 cm, 19 cm).
2. A = 2 cm:
In this case, B + C = 21 - 2 = 19 cm. We need to find pairs of values (B, C) that satisfy the inequality theorem.
Possible combinations: (10 cm, 9 cm), (9 cm, 10 cm), (8 cm, 11 cm), ..., (2 cm, 17 cm).
3. A = 3 cm:
In this case, B + C = 21 - 3 = 18 cm. We need to find pairs of values (B, C) that satisfy the inequality theorem.
Possible combinations: (10 cm, 8 cm), (9 cm, 9 cm), (8 cm, 10 cm), ..., (3 cm, 15 cm).
Continue this process for A = 4 cm, 5 cm, 6 cm, ..., up to A = 10 cm. Note that A cannot be larger than 10 cm, as the sum of the other two sides must be greater than A.
Repeat the same process for the second triangle.
Keep in mind that this will give you all the possible combinations of side lengths that are valid for the triangles.