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According to the figure ;
LK || IJ
If there are two parallel sides in a triangle, we can use the Thales theorem.
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According to the Thales theorem we have :
[tex] \frac{HL}{ LI } = \frac{HK}{KJ} \\ [/tex]
Thus :
[tex] \frac{16}{9} = \frac{24}{ KJ} \\ [/tex]
Multiply sides by KJ
[tex]KJ \times \frac{16}{9} = 24 \\ [/tex]
Multiply sides by 9
[tex]KJ \times 16 = 24 \times 9[/tex]
Divided sides by 16
[tex]KJ = \frac{24 \times 9}{16} \\ [/tex]
[tex]KJ = \frac{8 \times 3 \times 9}{8\times 2} \\ [/tex]
8 s simplifies
[tex]KJ = \frac{3 \times 9}{2} \\ [/tex]
[tex]KJ = \frac{27}{2} \\ [/tex]
[tex]KJ = \frac{26 + 1}{2} \\ [/tex]
[tex]KJ = \frac{26}{2} + \frac{1}{2} \\ [/tex]
[tex]KJ = 13 + 0.50[/tex]
[tex]KJ = 13.50[/tex]
Done....
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