Question : In $\triangle X Y Z, P$ is a point on side YZ and XY = XZ. If $\angle X P Y=90°$ and $Y P=9\ \text{cm}$, then what is the length of $YZ$?
Option 1: 17 cm
Option 2: 18 cm
Option 3: 12 cm
Option 4: 15 cm
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Correct Answer: 18 cm
Solution : The given triangle is isosceles. In $\triangle XPY$ and $\triangle XPZ$ $XY = XZ$ (given) $XP = XP$ (common) $\angle XPY = \angle XZY$ (isosceles triangle) $\triangle XPY \cong \triangle XPZ$ $\therefore YP=PZ=9\ \text{cm}$ $YZ=YP+PZ = 9+9=18\ \text{cm}$ Hence, the correct answer is 18 cm.
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