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In ∆PQR, ∠Q is right angle, S is the mid-point of the side PR. If PQ = 4 cm, QR = 6 cm, then the length of PS is
- a)3 cm
- b)√13 cm
- c)√5 cm
- d)8 cm
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In ∆PQR, ∠Q is right angle, S is the mid-point of the side P...
Using Pythagoras's theorem,
⇒ PR2 = PQ2 + QR2
⇒ PR2 = 42 + 62
⇒ PR = √52 cm = 2√13
⇒ PS = PR/2 = √13
⇒ PR2 = PQ2 + QR2
⇒ PR2 = 42 + 62
⇒ PR = √52 cm = 2√13
⇒ PS = PR/2 = √13
Most Upvoted Answer
In ∆PQR, ∠Q is right angle, S is the mid-point of the side P...
Given Information
- Triangle PQR is a right triangle with ∠Q as the right angle.
- Side lengths: PQ = 4 cm and QR = 6 cm.
- S is the midpoint of side PR.
Finding Length of PS
1. Calculate PR using the Pythagorean theorem:
- Since triangle PQR is a right triangle, we can apply the theorem:
\[
PR^2 = PQ^2 + QR^2
\]
\[
PR^2 = 4^2 + 6^2 = 16 + 36 = 52
\]
\[
PR = \sqrt{52} = 2\sqrt{13} \text{ cm}
\]
2. Determine the length of PS:
- Since S is the midpoint of PR:
\[
PS = \frac{PR}{2} = \frac{2\sqrt{13}}{2} = \sqrt{13} \text{ cm}
\]
Conclusion
The length of PS is thus calculated to be \(\sqrt{13}\) cm, which corresponds to option 'B'.
- Triangle PQR is a right triangle with ∠Q as the right angle.
- Side lengths: PQ = 4 cm and QR = 6 cm.
- S is the midpoint of side PR.
Finding Length of PS
1. Calculate PR using the Pythagorean theorem:
- Since triangle PQR is a right triangle, we can apply the theorem:
\[
PR^2 = PQ^2 + QR^2
\]
\[
PR^2 = 4^2 + 6^2 = 16 + 36 = 52
\]
\[
PR = \sqrt{52} = 2\sqrt{13} \text{ cm}
\]
2. Determine the length of PS:
- Since S is the midpoint of PR:
\[
PS = \frac{PR}{2} = \frac{2\sqrt{13}}{2} = \sqrt{13} \text{ cm}
\]
Conclusion
The length of PS is thus calculated to be \(\sqrt{13}\) cm, which corresponds to option 'B'.
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In ∆PQR, ∠Q is right angle, S is the mid-point of the side PR. If PQ = 4 cm, QR = 6 cm, then the length of PS isa)3 cmb)√13 cmc)√5 cmd)8 cmCorrect answer is option 'B'. Can you explain this answer?
Question Description
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In ∆PQR, ∠Q is right angle, S is the mid-point of the side PR. If PQ = 4 cm, QR = 6 cm, then the length of PS isa)3 cmb)√13 cmc)√5 cmd)8 cmCorrect answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about In ∆PQR, ∠Q is right angle, S is the mid-point of the side PR. If PQ = 4 cm, QR = 6 cm, then the length of PS isa)3 cmb)√13 cmc)√5 cmd)8 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In ∆PQR, ∠Q is right angle, S is the mid-point of the side PR. If PQ = 4 cm, QR = 6 cm, then the length of PS isa)3 cmb)√13 cmc)√5 cmd)8 cmCorrect answer is option 'B'. Can you explain this answer?.
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