Two sides of a triangle are 11cm and 16cm what is the range of possible lengths for the third side
third side --- x
by properties of sides of a triangle:
x+11>16 and x+16 > 11 and 11+16> x
x > 5 and x > -5 , (no argument there) and x < 27
so x > 5 and x < 27 or
5 < x < 27
in words: the third side must be greater than 5 but less than 27
the 3rd side must be shorter than the sum of the 1st two sides
... and longer than their difference
(11 + 16) > s > (16 - 11)
To find the range of possible lengths for the third side of a triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we have two sides of lengths 11cm and 16cm.
Let's consider the first scenario where the first side (11cm) and the second side (16cm) are added together, giving us a sum of 27cm. The third side must be shorter than the sum of the other two sides, so the third side must be less than 27cm.
Now, let's consider the second scenario where we subtract the smaller side (11cm) from the larger side (16cm). In this case, the difference is 5cm. The third side must be longer than the difference of the other two sides, so the third side must be greater than 5cm.
Therefore, the range of possible lengths for the third side is greater than 5cm and less than 27cm. In mathematical notation, we can represent this as:
5cm < third side < 27cm