Question

Theo draws XYZ XY has a length of 8 inches and Y Z has a length of 13 inches.

Determine whether each measurement could be the length of XZ.

Select Yes or No for each measurement

Answer 1

The possible measure of XZ must lie within 5 < XZ < 21

Sides of triangle

The theorem of the triangle is that the sum of any two sides must be greater than the third side

Given the following side

XY = 8in

YZ = 13in

XZ + XY > YZ
XZ + YZ > XY
YZ + XY > XZ

Substitute the given parameters

XZ + XY > YZ

XZ + 8 > 13
XZ > 5

Also, XZ + YZ > XY

XZ + 13 > 5
XZ > -8

Lastly, YZ + XY > XZ

13 + 8 > XZ
XZ < 21

Hence the possible measure of XZ must lie within 5 < XZ < 21

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