Question : In $\triangle X Y Z, \angle YXZ=90°$, P is a point on side YZ such that XP is perpendicular to YZ. If XP = YP = 10 cm then what will be the value of PZ?
Option 1: 8 cm
Option 2: 9 cm
Option 3: 12 cm
Option 4: 10 cm
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Correct Answer: 10 cm
Solution :
In $ΔXYZ$,
$\angle YXZ = 90°$
If $\angle Y = θ$, then $\angle Z = 90° - θ$
In $ΔXPY$,
$\angle YPX = 90°$ [Given]
⇒ $\angle Y = \angle YXP = θ$ [As XP = PY]
In $ΔXPZ$,
⇒ $\angle XPZ = 90°$ [Given]
⇒ $\angle PXZ = 90 - θ$
⇒ $\angle Z = 90 - θ$
Since two angles are equal, $ΔXPZ$ is an isosceles triangle.
⇒ XP = PZ = 10 cm
Hence, the correct answer is 10 cm.
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