Question 71 markMCQSection A

If ΔABC\Delta ABC and ΔDEF\Delta DEF are similar such that 2AB=DE2AB = DE and BC=8BC = 8 cm, then EF is equal to :

(a) 4 cm (b) 8 cm (c) 12 cm (d) 16 cm

Triangles
Similarity of Triangles - Ratio of Corresponding Sides

Options

(A)4 cm
(B)8 cm
(C)12 cm
(D)16 cm

Official answer

(d) 16 cm — since 2AB=DE2AB = DE, the scale factor ΔDEF:ΔABC\Delta DEF : \Delta ABC is 2, so EF=2×BC=2×8=16EF = 2 \times BC = 2 \times 8 = 16 cm.

Answer keywords:similar trianglescorresponding sidesproportionalityscale factorAB/DE = BC/EF16 cm

Marking scheme

  1. 1.1 mark: correct option (d) 16 cm, no method required for MCQ but full-credit reasoning is: AB/DE=BC/EF=1/2AB/DE = BC/EF = 1/2, hence EF=2×8=16EF = 2 \times 8 = 16 cm.

Hint

Use AB/DE=BC/EFAB/DE = BC/EF; since 2AB=DE2AB = DE, the scale factor is 2, so EF=2×BCEF = 2 \times BC.

Quick oral answer

In similar triangles, corresponding sides are in the same ratio; since DE is twice AB, every side of ΔDEF\Delta DEF is twice the corresponding side of ΔABC\Delta ABC, so EF=2×BC=16EF = 2 \times BC = 16 cm.

Common mistakes

  1. 1.Inverting the ratio and computing EF=BC/2=4EF = BC/2 = 4 cm instead of EF=2×BCEF = 2 \times BC.
  2. 2.Assuming similar triangles are always congruent and picking EF=BC=8EF = BC = 8 cm.
  3. 3.Not converting the relation '2AB=DE2AB = DE' correctly into a ratio AB:DE=1:2AB:DE = 1:2.

Analysis and explanation

Tests similarity of triangles and the proportionality of corresponding sides.


Concept

  • ΔABC∼ΔDEF\Delta ABC \sim \Delta DEF ⟹ corresponding sides are proportional: AB/DE=BC/EF=AC/DFAB/DE = BC/EF = AC/DF.
  • Given 2AB=DE2AB = DE, the ratio AB/DE=12AB/DE = \frac{1}{2}, so ΔDEF is exactly twice the size of ΔABC (scale factor 2).

Key points

  • Since BC/EF must also equal 1/2, EF=2×BC=2×8=16EF = 2 \times BC = 2 \times 8 = 16 cm.
  • Option (d) 16 cm is correct.

Common mistakes

  • Halving BC instead of doubling it (gives the wrong distractor 4 cm).
  • Assuming the triangles are congruent (ratio 1:11:1), which ignores the condition 2AB=DE2AB = DE and gives 8 cm.
  • Losing track of which triangle is 'larger' from the relation 2AB=DE2AB = DE, and inverting the ratio.

Interesting facts

The concept of similar triangles was foundational to Thales' method (c. 600 BCE) of measuring the height of the Great Pyramid of Giza using shadow lengths.

CBSE has asked ratio-of-sides questions on similar triangles in almost every board exam year since the introduction of the current syllabus, making it a high-frequency MCQ topic.

Question details

Q7 of 56 questions

Board
CBSE
Class
Class 10
Subject
Mathematics (Standard)
Year
2026
Section
Section A
Marks
1
Type
MCQ
Chapter
Triangles
Topic
Similarity of Triangles - Ratio of Corresponding Sides
Bloom's level
apply
Syllabus topic
Unit 2: Geometry — Triangles: Areas/Sides of Similar Triangles (Basic Proportionality)
Author
CBSE
Reviewed by
Padhantu Academic Team

Spotted a mistake or something unclear?

Tell us and we will fix it.

Frequently asked questions

How do you find an unknown side in similar triangles?

Set up the ratio of corresponding sides using the similarity statement (e.g., ΔABC∼ΔDEF\Delta ABC \sim \Delta DEF gives AB/DE=BC/EF=AC/DFAB/DE = BC/EF = AC/DF) and solve for the unknown using cross-multiplication.

Why does the order of letters in ΔABC∼ΔDEF\Delta ABC \sim \Delta DEF matter?

The order tells you which vertices (and hence sides) correspond: A↔D,B↔E,C↔FA \leftrightarrow D, B \leftrightarrow E, C \leftrightarrow F, so side AB corresponds to DE and BC corresponds to EF.