Question

The lengths of the sides of triangle XYZ are written in terms of the variable m, where m ≥ 6.

Triangle X Y Z is shown. The length of side X Y is m + 8, the length of side Y Z is 2 m + 3, the length of side Z X is m minus 3.

Which is correct regarding the angles of the triangle?

mAngleX < mAngleZ < mAngleY
mAngleY < mAngleZ < mAngleX
mAngleY < mAngleX < mAngleZ
mAngleZ < mAngleY < mAngleX

Answer 1

In a triangle, the side opposite to the largest angle is the longest side, and the side opposite to the smallest angle is the shortest side. In triangle XYZ, the length of side XY is m + 8, the length of side YZ is 2m + 3, and the length of side ZX is m - 3. Since m ≥ 6, we can determine that 2m + 3 is the largest value, m + 8 is the next largest value, and m - 3 is the smallest value. Therefore, side YZ is the longest side and side ZX is the shortest side.

Since side YZ is the longest side, angle X must be the largest angle. Since side ZX is the shortest side, angle Y must be the smallest angle. Therefore, the correct ordering of the angles from smallest to largest is ∠Y < ∠Z < ∠X.

Explanation: