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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?

Respuesta :

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

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

Then the measurement IJ is:

[tex]IJ=62-3x=62-(3\cdot8)=62-24=38[/tex]

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