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△ AHK ~ △ ABC. If AK = 10 cm… (Class 10 Maths 2026, Q22a)

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MathsCBSE Class 10 · Standard · Board exam 2026, set 30/2/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 22(a)

Set in the CBSE Class 10 board exam of 2026, paper 30/2/1, section B, question 22(a), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q22(a) · 2 marks · Very short answerTriangles

In the given figure, . If AK = 10 cm, BC = 3·5 cm and HK = 7 cm, find the length of AC.

Figure in the paper: Figure: Points H (top right), A (on a line), K (bottom right) form right triangle AHK with HK vertical and AK horizontal. Points C (left), A and K lie on one horizontal line; B lies below C, and segment BA extended meets H. Triangle ABC has right angle at C; BC is vertical and CA is horizontal. Labels: C, A, B, H, K. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/2/1.

Hints

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

Hint 1

Match the vertices in order: A with A, H with B, K with C.

Hint 2

AK corresponds to AC and HK corresponds to BC; set their ratios equal.

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. Since (A↔A, H↔B, K↔C), the corresponding sides are proportional:

    1 mark

  2. ½ mark

  3. cm

    ½ mark

Answer: AC = 5 cm

Where the marks are

  • Writes the correct ratio of corresponding sides (1 mark)
  • Substitutes the given values (½ mark)
  • Gets AC = 5 cm (½ mark)

Revise the chapter

  • Chapter: Triangles (notes, formulas, where marks are lost and every past question)
Practise this chapterBoard-style questions from Triangles, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/2/1 (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.