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

CBSE Class 10 Mathematics Standard 2023: question 12

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, section A, question 12, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q12 · 1 mark · MCQTriangles

In the given figure, $△ A B C \sim △ QP R$ . If AC = 6 cm, BC = 5 cm, QR = 3 cm and PR = x; then the value of x is:

(A)3.6 cm
(B)2.5 cm
(C)10 cm
(D)3.2 cm

Figure in the paper: Two triangles side by side. Triangle ABC: vertices A (top left), C (top right), B (bottom). AC = 6 cm (top side), BC = 5 cm (slanted side). Triangle QPR: vertices R (top), Q (bottom left), P (bottom right). QR = 3 cm (left slanted side), PR = x (right slanted side). Base QP is horizontal. 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

Match the vertices in the order they are written in the similarity statement.

Hint 2

AC corresponds to QR and BC corresponds to PR. 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.

From $△ A B C \sim △ QP R$ the vertices correspond as $A \leftrightarrow Q$ , $B \leftrightarrow P$ , $C \leftrightarrow R$ . So $A C \leftrightarrow QR$ and $B C \leftrightarrow P R$ .
$\frac{A C}{QR} = \frac{B C}{P R} \Rightarrow \frac{6}{3} = \frac{5}{x}$ .
$x = \frac{5 \times 3}{6} = 2.5$ cm. So the answer is option (B).
1 mark

Answer: 2.5 cm, option (B)

Where the marks are

Chooses option (B) 2.5 cm (1 mark)

Revise the chapter

Chapter: Triangles (notes, formulas, where marks are lost and every past question)
Topic: Problems on Similar Triangles

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.

CBSE Class 10 Mathematics Standard 2023: question 12

Hints

Step-by-step solution

Revise the chapter

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