Answer:
2
Explanation:
Corresponding sides are proportional in these similar triangles.
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short side/long side = k/4 = 4/8
k = 4(4/8) . . . . multiply by 4
k = 2
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Additional comment
The lengths of the hypotenuses can be found the same way, or using the Pythagorean theorem. Using side ratios, we have ...
l² = k(k+8) = 2(10) = 20 . . . . from MN/MO = ML/MN
l = 2√5
m² = 8(8+2) = 80 . . . . from LN/LO = LM/LN
m = 4√5
The similarity statements are ...
ΔLMN ~ ΔLNO ~ ΔNMO