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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