Question : In $\triangle \mathrm{PQR}, \angle \mathrm{Q}=90$°, and QX is perpendicular to PR. If PQ = 15 cm and PR = 25 cm, what is the PX : XR ratio?
Option 1: 2 : 3
Option 2: 7 : 18
Option 3: 1 : 4
Option 4: 9 : 16
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
Correct Answer: 9 : 16
Solution :
If a perpendicular is drawn from the vertex of the right angle of a right-angled triangle to the hypotenuse, then it divides the hypotenuse into two segments.
The lengths of these segments are proportional to the lengths of the other two sides.
This is based on the principle of similar triangles.
Using the principle of similar triangles, since $\triangle$PQR ~ $\triangle$PQX, we have:
$\frac{PX}{PQ}$ = $\frac{PQ}{PR}$
Plugging in the given values:
$\frac{PX}{15}$ = $\frac{15}{25}$
$\therefore$ PX = 9 cm
So, XR = PR – PX = 25 – 9 = 16
Therefore, the ratio of PX to XR is 9 : 16.
hence, the correct answer is 9 : 16.
Related Questions
Know More about
Staff Selection Commission Combined High ...
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Get Updates Brochure
Your Staff Selection Commission Combined Higher Secondary Level Exam brochure has been successfully mailed to your registered email id “”.
