1 markMCQSection A

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

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

Q: If $\Delta ABC$ and $\Delta DEF$ are similar such that $2AB = DE$ and $BC = 8$ cm, then EF is equal to : (a) 4 cm (b) 8 cm (c) 12 cm (d) 16 cm

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

Triangles

Similarity of Triangles - Ratio of Corresponding Sides

Options

(A)4 cm

(B)8 cm

(D)16 cm

Official Answer

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

similar trianglescorresponding sidesproportionalityscale factorAB/DE = BC/EF16 cm

Marking Scheme

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

Hint

Use $AB/DE = BC/EF$ ; since $2AB = DE$ , the scale factor is 2, so $EF = 2 \times BC$ .

Quick Oral Answer

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

Analysis & Explanation

Tests similarity of triangles and the proportionality of corresponding sides.

Concept

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

Key points

Since BC/EF must also equal 1/2, $EF = 2 \times BC = 2 \times 8 = 16$ 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 $1:1$ ), which ignores the condition $2AB = DE$ and gives 8 cm.
Losing track of which triangle is 'larger' from the relation $2AB = DE$ , and inverting the ratio.

Common Mistakes

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

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.

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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., $\Delta ABC \sim \Delta DEF$ gives $AB/DE = BC/EF = AC/DF$ ) and solve for the unknown using cross-multiplication.

Why does the order of letters in $\Delta ABC \sim \Delta DEF$ matter?

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