The correct answers are Options A, D, and F.
Identifying the possible length of the third side in a triangle:
Given:
The lengths of the triangle are 4 and 7.
Let's assume the length of each side of the triangle to be x, y, and z.
With the given condition, let's say x=4 and y=7 and z= 3rd side.
A triangle must satisfy a condition that the sum of its 2 sides is always greater than the 3rd side.
As we are unsure which side is the greatest in the given triangle, let's apply the values for each of the conditions.
If z is longer, then x+y >z
Applying the values of x and y, 11 > z
If y is longer, then x+z > y
Applying the values of x and y,
4 + z >7
z > 7-4
z > 3
From the above, it is clear that 3<z<11.
Hence, any value between 3 and 11 can satisfy this triangle.
Therefore, the correct answer from the given options is 5, 7, and 9.
#SPJ2
