Question : In $ riangle X Y Z, P$ is a point on side YZ and XY = XZ. If $\angle X P Y=90°$ and $Y P=9\ ext{cm}$, then what is the length of $YZ$?
Option 1: 17 cm
Option 2: 18 cm
Option 3: 12 cm
Option 4: 15 cm

Question

Question : In $ riangle X Y Z, P$ is a point on side YZ and XY = XZ. If $\angle X P Y=90°$ and $Y P=9\ ext{cm}$, then what is the length of $YZ$?

Option 1: 17 cm

Option 2: 18 cm

Option 3: 12 cm

Option 4: 15 cm

Team Careers360 · Accepted Answer

Correct Answer: 18 cm

Solution :
The given triangle is isosceles.
In $ riangle XPY$ and $ riangle XPZ$
$XY = XZ$ (given)
$XP = XP$ (common)
$\angle XPY = \angle XZY$ (isosceles triangle)
$ riangle XPY \cong riangle XPZ$
$ herefore YP=PZ=9\ ext{cm}$
$YZ=YP+PZ = 9+9=18\ ext{cm}$
Hence, the correct answer is 18 cm.

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Question : In △XYZ,P is a point on side YZ and XY = XZ. If ∠XPY=90° and YP=9 cm, then what is the length of YZ?Option 1: 17 cmOption 2: 18 cmOption 3: 12 cmOption 4: 15 cm

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Question : In $△ X Y Z, P$ is a point on side YZ and XY = XZ. If $∠ X P Y = 90 °$ and $Y P = 9 cm$ , then what is the length of $Y Z$ ?
Option 1: 17 cm
Option 2: 18 cm
Option 3: 12 cm
Option 4: 15 cm