In the given figure, DE ∥ BC. The value of x is : (A) 6 (B) 12·5 (C) 8 (D) 10

MathsCBSE Class 10 · Standard · Board exam 2023, set 30/5/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard 2023: question 4

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, section A, question 4, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q4 · 1 mark · MCQTriangles

In the given figure, $D E ∥ B C$ . The value of x is :

(A)6
(B)12·5
(C)8
(D)10

Figure in the paper: Triangle ABC with D on side AB and E on side AC, DE parallel to BC. AD = 2 cm, DB = 3 cm, DE = 4 cm, BC = x 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 30/5/1.

Hints

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

Hint 1

Which two triangles are similar when $D E ∥ B C$ ?

Hint 2

Note $A B = A D + D B = 5$ cm, not 3 cm.

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.

$D E ∥ B C \Rightarrow △ A D E \sim △ A B C$ (AA), so $\frac{A D}{A B} = \frac{D E}{B C}$ .
$\frac{2}{5} = \frac{4}{x} \Rightarrow x = 10$ . Option (D).
1 mark

Answer: x = 10, option (D)

Where the marks are

Uses similarity with $A B = 5$ cm to get $x = 10$ (1 mark)

Revise the chapter

Chapter: Triangles (notes, formulas, where marks are lost and every past question)
Topic: Basic Proportionality Theorem (Thales Theorem)

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 30/5/1 (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 4

Hints

Step-by-step solution

Revise the chapter

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