Question

If LM= 20cm, and PQ= 16cm, what is the length of RM

Answer 1

Check the picture below.

so hmmm let's use the pythagorean theorem, since the angle at R is a right-angle

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{10}\\ a=\stackrel{adjacent}{8}\\ o=\stackrel{opposite}{10-x} \end{cases} \\\\\\ (10)^2= (8)^2 + (10-x)^2\implies 100=64+\stackrel{ F~O~I~L }{(100-20x+x^2)} \\\\\\ 100=x^2-20x+164\implies 0=x^2-20x+64 \\\\\\ 0=(x-16)(x-4)\implies RM=x= \begin{cases} 16 ~~ \bigotimes\\ 4 ~~ ~~ \checkmark \end{cases}`

now, why x ≠ 16? well, diameter is 20, so the radius is 10, there's no way RM is going to be larger than 10 or even 10.