Question

What is JL if KM=6?



Not really much context but that’s the whole question

Answer 1

Explanation:

geometric mean theorem :

the height of a right-angled triangle to the Hypotenuse is the square root of the product of the parts of the Hypotenuse (as the height splits the Hypotenuse into 2 parts : JM and ML).

JL = JM + ML

in short

KM = sqrt(JM × ML)

6 = sqrt(8 × ML)

36 = 8 × ML

ML = 36/8 = 9/2 = 4.5

so,

JL = JM + ML = 8 + 4.5 = 12.5

Answer 2

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.

`\cfrac{x}{6}=\cfrac{6}{8}\implies \cfrac{x}{6}=\cfrac{3}{4}\implies x=\cfrac{18}{4}\implies x=\cfrac{9}{2} \\\\[-0.35em] ~\dotfill\\\\ 8+x\implies 8+\cfrac{9}{2}\implies \cfrac{25}{2}\implies 12(1)/(2)=JL`