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
New: SSC CHSL Tier 2 answer key released | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
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.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
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 $YZ$?
Question : Two similar triangles are given i.e. $\triangle$LMN ~ $\triangle$PQR, with measurement of angle and side as $\angle$ L = 40°, $\angle$ N = 80°, LM = 6 cm, LN = 8 cm and PQ = 7.5 cm. Find the value of $\angle$ Q and side PR, respectively.
Question : X, Y, and Z are three equilateral triangles. The sum of the areas of X and Y is equal to the area of Z. If the side lengths of X and Y are 6 cm and 8 cm respectively, then what is the side length of Z?
Question : M is the incentre of the $\triangle $XYZ. If $\angle $YXZ + $\angle $YMZ = 150°, then what is the value of $\angle $YXZ?
Question : In a triangle the length of the opposite side of the angle which measures 45° is 8 cm, what is the length of the side opposite to the angle which measures 90°?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile