Question

Please show your work thank you

Answer 1

 

$\displaystyle\\\frac{LM}{QP}=\frac{NL}{RQ}\\\\\frac{8}{12}=\frac{x+7}{2x+5}\\\\8(2x+5)=12(x+7)\\16x+40=12x+84\\16x-12x=84-40\\4x=44\\\\x=\frac{44}{4}\\\\\boxed{x=11}\\RQ=2\cdot11+5=22+5\\\boxed{\bf RQ=27~~correct~answer: ~C.}\\\\NL=11+7 = 18\\MN=11+5=16\\PR=2\cdot11+2=22+2=24$