triangle xyz. find all possible lengths of xy
given:
xz:9in
yz:5in
given:
xz=1
yz=13
To find all possible lengths of side XY in triangle XYZ, 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 remaining side.
Given:
XZ = 9in
YZ = 5in
To find the possible lengths of XY, we need to consider the sum of the lengths of XZ and YZ:
XY < XZ + YZ
XY < 9in + 5in
XY < 14in
Therefore, the maximum possible length for XY is 14in.
Now let's consider the second given scenario:
XZ = 1in
YZ = 13in
Again, we can use the triangle inequality theorem:
XY < XZ + YZ
XY < 1in + 13in
XY < 14in
Here as well, the maximum possible length for XY is 14in.
In both scenarios, the maximum possible length for XY is 14in. However, the minimum length of XY is not provided, so we cannot determine the full range of possible lengths for XY without additional information.