In ΔXYZ, ∠YXZ = 90 degree. P is a point on side YZ such that XP is perpendicular to YZ. If XP = YP = 10 cm, then what will be value of PZ?
Answer & explanation
Correct answer: option 4
We have,
∠YXZ = 90 degree
XP = YP = 10 cm
In ΔXYZ,
∠YXZ = 90 degree
If ∠Y = θ , then
=∠Z = 90 - θ
In ΔXPY,
=∠YPX = 90° [Given]
=∠Y = ∠YXP = θ [XP = PY]
In ΔXPZ,
= ∠XPZ = 90° [Given]
= ∠PXZ = 90 - θ
⇒ ∠Z = 90 - θ
ΔXPZ is isosceles triangle. Then, = XP = PZ = 10 cm