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If ∠ PQR = ∠ QSP, PQ =… (Class 10 Maths SQP 2026-27, Q22B)

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MathsCBSE Class 10 · Standard · Sample paper, session 2026-27 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 22(B)

From the official CBSE sample question paper for 2026-27, section B, question 22(B), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(B) · 2 marks · Very short answerTriangles

In the given figure, if , PQ = 6 cm and PS = 3 cm, then find the length of PR.

For visually impaired candidates: In a right-angled triangle ABC, right-angled at B, a perpendicular BD is drawn to the hypotenuse AC. Prove that the triangle BCD is similar to the triangle ACB.

Figure in the paper: Triangle PQR with a point S on side PR; segment QS joins Q to S. Angle PQR (at Q) and angle QSP (at S) are marked as equal. PQ = 6 cm and PS = 3 cm are given; PR is to be found. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

Open one hint at a time and try again before the next.

Hint 1

Angle P is common to both triangle PQR and triangle PSQ.

Hint 2

Match the vertices carefully: Q in ΔPQR corresponds to S in ΔPSQ.

Hint 3

Use PQ/PS = PR/PQ.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. In and : (given) and (common).

    ½ mark

  2. [AA criterion], with , , .

    ½ mark

  3. Corresponding sides are proportional: .

    ½ mark

  4. cm.

    ½ mark

  5. For visually impaired candidates (this alternative carries the same 2 marks: ½ + ½ + 1). In and : [, and the triangle is right-angled at B].

  6. (common angle C).

  7. [AA criterion]. Hence proved.

Answer: PR = 12 cm (VI version: ΔBCD ~ ΔACB by AA)

Where the marks are

  • Equal angle pair given and common angle P (½ mark)
  • Concludes ΔPQR ~ ΔPSQ by AA (½ mark)
  • Writes PQ/PS = PR/PQ with values (½ mark)
  • PR = 12 cm (½ mark)
  • VI alternative: right angles equal (½ mark), common angle C (½ mark), AA similarity concluded (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2026-27 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.