Question

4.Trapezoid STUV is similar to trapezoid NOPQ (8.3A)U18 cmvN12 cm6 cmo14 cmS?What is the length of Op?A.4 centimetersB.5 centimetersC.28 centimetersD.36 centimeters

Answer 1

From the figures, STUV is similar to NOPQ

So their sides are proportion

$\frac{UV}{PQ}=\frac{ST}{NO}=\frac{UT}{OP}$

Since UT = 12

NO = 6

ST = 14

Let us substitute them in the rule above

$\frac{18}{PQ}=\frac{14}{6}=\frac{12}{OP}$

By using cross multiplication with the last two fraction

$\begin{gathered} \frac{14}{6}=\frac{12}{OP} \\ 14\times OP=6\times12 \\ 14OP=72 \end{gathered}$

Divide both sides by 14 to find OP

$\begin{gathered} \frac{14OP}{14}=\frac{72}{14} \\ OP=\frac{36}{7}=5\frac{1}{7} \end{gathered}$

Answer B