The semi perimeter of a triangle is 10 cm .If one of its sides is 5 cm and 7 cm respectively then its third side is
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To find the length of the third side of the triangle, we can use the formula for the perimeter of a triangle, which is the sum of all three sides.
The semi-perimeter (s) of a triangle is half of the perimeter. In this case, the semi-perimeter (s) is given as 10 cm.
To find the perimeter (P) of the triangle, we can use the formula P = 2s. Substituting the given value, we have:
P = 2s = 2 * 10 cm = 20 cm
Now we know that the perimeter of the triangle is 20 cm.
We are also given the lengths of two sides, which are 5 cm and 7 cm respectively.
Let's assume that the length of the third side is x cm.
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.
Using this inequality, we can set up the following equation:
5 cm + 7 cm > x cm
12 cm > x cm
So, the third side must be less than 12 cm.
However, we also know that the sum of all three sides of a triangle is equal to the perimeter. Therefore, we can set up another equation:
5 cm + 7 cm + x cm = 20 cm
12 cm + x cm = 20 cm
Subtracting 12 cm from both sides of the equation, we get:
x cm = 20 cm - 12 cm
x cm = 8 cm
Therefore, the length of the third side of the triangle is 8 cm.