Answer:
see explanation
Step-by-step explanation:
Since the triangles in both cases are similar then the ratios of corresponding sides are equal.
(1)
[tex]\frac{EF}{HJ}[/tex] = [tex]\frac{FG}{JG}[/tex], substitute values
[tex]\frac{5}{3}[/tex] = [tex]\frac{x+9}{9}[/tex] ( cross- multiply ) ← proportion
3(x + 9) = 45 ( divide both sides by 3 )
x + 9 = 15 ( subtract 9 from both sides )
x = 6
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(2)
[tex]\frac{LM}{NM}[/tex] = [tex]\frac{KM}{LM}[/tex], substitute values
[tex]\frac{6}{5}[/tex] = [tex]\frac{x+5}{6}[/tex] ( cross- multiply ) ← proportion
5(x + 5) = 36 ( divide both sides by 5 )
x + 5 = 7.2 ( subtract 5 from both sides )
x = 2.2
