find the length of the third side of a triangle with a perimeter of 21 in. if the sum of the other 2 sides is 15in.
Let the lengths of the other two sides be x and 15 - x.
According to the triangle inequality, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Therefore, we have the following inequality:
x + (15 - x) > 21 - (x + 15 - x)
Simplifying the inequality, we get:
15 > 21 - 15
15 > 6
Since the inequality is true, the given triangle is possible.
Now, we need to find the length of the third side.
Using the information given that the sum of the other two sides is 15, we have:
x + (15 - x) = 15
x + 15 - x = 15
15 = 15
Therefore, there is no information given that allows us to determine the length of the third side. Additional information is needed.
To find the length of the third side of a triangle, you can use the fact that 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 the length of the third side is "x" inches.
Given that the perimeter of the triangle is 21 inches, we can write the equation:
Length of first side + Length of second side + Length of third side = Perimeter
x + (15 - x) + x = 21
Simplifying the equation:
2x + 15 = 21
Subtracting 15 from both sides:
2x = 21 - 15
2x = 6
Dividing both sides by 2:
x = 3
Therefore, the length of the third side of the triangle is 3 inches.
To find the length of the third side of a triangle, you can use the triangle inequality theorem. According to this theorem, for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
In this case, you are given the perimeter of the triangle, which is 21 inches, and the sum of the other two sides, which is 15 inches.
Let's assume the length of the third side is represented by 'x'.
According to the triangle inequality theorem, we have the following inequality:
15 + x > 21 - This is because the sum of the two shorter sides must be greater than the longest side.
Simplifying the inequality, we have:
x > 6
Therefore, the length of the third side must be greater than 6 inches.
However, we need to remember that the third side cannot be longer than the sum of the two shorter sides. So, the maximum length of the third side would be 15 - 6 = 9 inches.
Hence, the length of the third side of the triangle must be greater than 6 inches but less than or equal to 9 inches.