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Find the length of the perpendicular from R to KO when R (3 , 4), K ( 3 , 1) and O ( 8 , 4) are the vertices of a right-angled triangle.
What you have here is a right triangle with legs of 5(RO) and 3(RK) and a hypotenuse (OK).
Using the pythagorean theorem, OK = sqrt(5^2+3^2)=sqrt(34)
Let x=length of the perpendicular from R to KO, and P, the point at which the perpendicular lands on KO.
We can now see two similar triangles: the first is the larger one,RKO, and a smaller,RKP of which x is one of the legs. We can now set up a proportion.