Question

Triangle ABC is similar to triangle DEF. Find the measure of side EF. Round youranswer to the nearest tenth. Figures are not drawn to scale.

Answer 1

Since triangles ABC and DEF are similar, then their corresponding sides has an equal ratio (They are proportion)

$\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$

Since AB = 11 and BC = 23 and ED = 43

Substitute them in the ratio above

$\frac{11}{43}=\frac{23}{EF}$

By using the cross multiplication

$\begin{gathered} 11\times EF=43\times23 \\ 11EF=989 \end{gathered}$

Divide both sides by 11 to find EF

$\begin{gathered} \frac{11EF}{11}=\frac{989}{11} \\ EF=89.9090909 \end{gathered}$

Round it to the nearest tenth

EF = 89.9