The length of a triangle are 4cm and 7cm what is the measure of the third side
No way to tell, unless the triangle is a right triangle, in which case the third side is either
√(7^2-4^2) = √33
or
√(7^2+4^2) = √65
All we really can say is that if the third side has length x, then
7-4 < x < 7+4
3 < x < 11
To find the measure of the third side of a triangle, we can use the triangle inequality theorem. According to this 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 assume that the lengths of the sides are a, b, and c. In this case, we have two given side lengths: 4cm and 7cm. So, we can set up the following inequality:
4 + 7 > c
Now, we can simplify the equation:
11 > c
Therefore, the measure of the third side must be less than 11cm.
To find the measure of the third side of a triangle, you need to know the lengths of the other two sides.
The triangle inequality theorem states that in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's apply this theorem to the given lengths of 4cm and 7cm.
We need to consider two cases:
1. The sum of the lengths of the two sides is greater than the length of the third side:
4 + 7 = 11 (which is greater than the third side)
In this case, since the sum of the two sides is greater than the third side, a valid triangle can be formed. So, we have enough information to find the measure of the third side.
2. The sum of the lengths of the two sides is not greater than the length of the third side:
4 + 7 = 11 (which is equal to the third side)
In this case, since the sum of the two sides is equal to the third side, a degenerate triangle (a straight line) is formed. The third side has no length because it coincides with the other two sides.
Therefore, based on the given lengths of 4cm and 7cm, the measure of the third side can vary depending on the specific case.