1 markMCQSection A

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

Q: 7. If $\triangle ABC$ and $\triangle DEF$ are similar such that $2AB = DE$ and $BC = 8\text{ cm}$, then EF is equal to : (a) 4 cm (b) 8 cm (c) 12 cm (d) 16 cm

(d) 16 cm — since $DE = 2AB$, the scale factor is 2, so $EF = 2 \times BC = 2 \times 8 = 16\text{ cm}$.

Q: How do I know which triangle is bigger from $2AB = DE$?

Rearrange it as $DE = 2AB$. Since DE (a side of DEF) equals twice AB (a side of ABC), triangle DEF is the enlarged one, so all its sides are double the corresponding sides of ABC.

Triangles

Ratio of sides of similar triangles

Options

(A)4 cm

(B)8 cm

(D)16 cm

Official Answer

(d) 16 cm — since $DE = 2AB$ , the scale factor is 2, so $EF = 2 \times BC = 2 \times 8 = 16\text{ cm}$ .

similar trianglescorresponding sidesratio of sidesEF = 16 cmscale factor 2AB DE proportion

Marking Scheme

11 mark: correct option (d) 16 cm.
2Full credit requires only the correct choice; internally the ratio $\frac{DE}{AB} = 2$ giving $EF = 2 \times 8 = 16\text{ cm}$ justifies it.

Hint

$2AB = DE$ means DE is twice AB, so DEF is the bigger triangle; scale BC up by the same factor.

Quick Oral Answer

Because 2 AB equals DE, the scale factor from ABC to DEF is 2, so EF is twice BC, that is 2 into 8, which gives 16 cm.

Analysis & Explanation

Since $\triangle ABC \sim \triangle DEF$ and $2\cdot AB = DE$ , every side of △DEF is exactly double the matching side of △ABC — so $EF = 2 \times BC = 16\text{ cm}$ .

Concept

In similar triangles, corresponding sides are proportional: $\frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}$ .
$2AB = DE \Rightarrow \frac{DE}{AB} = 2$ , so $\triangle DEF$ is the enlarged triangle (scale factor 2), not the smaller one.

Key steps

BC corresponds to EF (both are the "middle" sides in the same vertex order).
$EF = 2 \times BC = 2 \times 8 = 16\text{ cm}$ → option (d).

Common mistakes

(a) 4 cm: wrongly halves BC, treating ABC as the larger triangle.
(b) 8 cm: assumes congruence (ratio 1), ignoring the factor 2.
(c) 12 cm: a distractor with no valid derivation.

Real-world

This is exactly the logic used in scale models and map enlargements — doubling every length keeps the shape identical while scaling the size.

Common Mistakes

1Reading $2AB = DE$ as AB being the larger side and dividing 8 by 2 to get 4 cm.
2Ignoring the factor of 2 and assuming $EF = BC = 8\text{ cm}$ because the triangles are 'similar' (confusing similar with congruent).
3Matching the wrong pair of corresponding sides (e.g. pairing BC with DF instead of EF).

Interesting Facts

The idea of similar triangles was used by the Greek mathematician Thales around 600 BCE to measure the height of the Egyptian pyramids using their shadows.

A scale factor of 2 in lengths gives a scale factor of 4 in area and 8 in volume — a fact every architect and 3D-model maker relies on.

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Frequently Asked Questions

How do I know which triangle is bigger from $2AB = DE$ ?

Rearrange it as $DE = 2AB$ . Since DE (a side of DEF) equals twice AB (a side of ABC), triangle DEF is the enlarged one, so all its sides are double the corresponding sides of ABC.

Which side of DEF corresponds to BC of ABC?

Because the similarity is written $\triangle ABC \sim \triangle DEF$ , vertices correspond in order: $A\leftrightarrow D, B\leftrightarrow E, C\leftrightarrow F$ . Therefore BC corresponds to EF, and $AB\leftrightarrow DE, CA\leftrightarrow FD$ .

Does 'similar' mean the triangles are the same size?

No. Similar means same shape (equal angles) but not necessarily the same size. Same size and shape is 'congruent', which would need the ratio to be 1, not 2.