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In △ ABC, PQ ∥ BC. If PB = 6… (Class 10 Maths 2023, Q16)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/4/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 16

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, section A, question 16, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q16 · 1 mark · MCQTriangles

In , . If PB = 6 cm, AP = 4 cm, AQ = 8 cm, find the length of AC.

  1. (A)12 cm
  2. (B)20 cm
  3. (C)6 cm
  4. (D)14 cm

Figure in the paper: Triangle ABC with A at the top. P lies on side AB and Q lies on side AC, with PQ drawn horizontally parallel to base BC. Marked lengths: PB = 6 cm, AP = 4 cm, AQ = 8 cm. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/4/1.

Hints

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

Hint 1

A line parallel to one side of a triangle divides the other two sides in the same ratio.

Hint 2

Find QC first, then add it to AQ.

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 , by the Basic Proportionality Theorem .

  2. cm.

  3. cm. So the answer is option (B).

    1 mark

Answer: 20 cm, option (B)

Where the marks are

  • Chooses option (B) 20 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 paper2023 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.