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△ AHK ~ △ ABC. If AK = 8 cm, BC… (Class 10 Maths 2024, Q25)

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MathsCBSE Class 10 · Standard · Board exam 2024, set 30/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2024: question 25

Set in the CBSE Class 10 board exam of 2024, paper 30/4/1, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerTriangles

In the given figure, AHK ABC. If AK = 8 cm, BC = 3.2 cm and HK = 6.4 cm, then find the length of AC.

Figure in the paper: A horizontal line through C, A and K (C on the left, K on the right). Point B lies vertically below C, with BC drawn vertically and a right angle at C. Point H lies vertically above K, with HK vertical and a right angle at K. The line from B passes through A and continues up to H. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 30/4/1.

Hints

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

Hint 1

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

Hint 2

So HK corresponds to BC and AK corresponds to AC; set up the ratio.

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 , corresponding sides are proportional:

    1 mark

  2. cm

    1 mark

Answer: AC = 4 cm

Where the marks are

  • Writes correct ratio of corresponding sides and substitutes (1 mark)
  • AC = 4 cm (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 paper2024 board paper, set 30/4/1 (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.