Answer:
BC = 1 [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{BC}{EF}[/tex] = [tex]\frac{AB}{DE}[/tex] ( substitute values )
[tex]\frac{BC}{4}[/tex] = [tex]\frac{\frac{3}{4} }{\frac{5}{2} }[/tex] ( 2 [tex]\frac{1}{2}[/tex] = [tex]\frac{5}{2}[/tex] )
cross- multiply
[tex]\frac{5}{2}[/tex] BC = 4 × [tex]\frac{3}{4}[/tex] = 3 ( multiply both sides by 2 to clear the fraction )
5 BC = 6 ( divide both sides by 5 )
BC = [tex]\frac{6}{5}[/tex] = 1 [tex]\frac{1}{5}[/tex]
