Answer: 12 cm
Step-by-step explanation:
[tex]\mathtt{Using\ the \ pythagorean \ theorem: \\}[/tex]
[tex]a^2+b^2=c^2, \\\ we\ can\ plug\ in\ values\ for\ a,\ b,\ and\ c[/tex]
[tex]L=a\ and\ M=b\ and\ N=c[/tex]
Therefore,
[tex]L^2+35^2=37^2\\L^2+1225=1369\\L^2=144\\\sqrt{L^2} =\sqrt{144} \\L=\pm12\\Taking\ only\ the\ positive\ answer,\ we\ get:\\\large\boxed{L = 12cm}[/tex]
