Answer:
x ≈ 7.2
Step-by-step explanation:
Δ MNO and Δ MKL are similar, so the corresponding sides are in proportion, that is
[tex]\frac{MN}{MK}[/tex] = [tex]\frac{MO}{ML}[/tex] , substitute values
[tex]\frac{13.1}{13.1+10.9}[/tex] = [tex]\frac{8.7}{8.7 +x}[/tex]
[tex]\frac{13.1}{24}[/tex] = [tex]\frac{8.7}{8.7+x}[/tex] ( cross- multiply )
13.1(8.7 + x) = 208.8 ← distribute left side
113.97 + 13.1x = 208.8 ( subtract 113.97 from both sides )
13.1x = 94.83 ( divide both sides by 13.1 )
x = [tex]\frac{94.83}{13.1}[/tex] ≈ 7.2 ( to the nearest tenth )
