Question

In the diagram below of triangle IJK, L is the midpoint of IK and M is themidpoint of JK . If LM = 5x – 21, and IJ = 62 - 3x, what is the measure ofIJ?

Answer 1

The triangles are similar and one can assume that LM and IJ have a ratio 2:1.

`\begin{gathered} 2\cdot LM=IJ \\ 2\cdot(5x-21)=62-3x \\ 10x-42=62-3x \\ 10x+3x=62+42 \\ 13x=104 \\ x=(104)/(13)=8 \end{gathered}`

Then the measurement IJ is:

`IJ=62-3x=62-(3\cdot8)=62-24=38`