ΔABC and ΔDEF are similar triangles and their areas are 49 cm² and 144 cm² respectively. If EF = 16.80 cm, then find BC.

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 2)

Answer 1

Given:

ΔABC and ΔDEF are similar triangles and their areas are 49 cm2 and 144 cm2 respectively.

EF = 16.80 cm

Concept used:

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

Calculation:

Since ΔABC and ΔDEF are similar triangles,

\(\frac {AB}{DE} = \frac {BC}{EF} = \frac {AC}{DF} = \sqrt { \frac {area (\Delta ABC)}{area (\Delta DEF)}}\)

⇒ \(\frac {BC}{EF} = \sqrt { \frac {area (\Delta ABC)}{area (\Delta DEF)}}\)

⇒ \(\frac {BC}{16.80} = \sqrt { \frac {49}{144} }\)

⇒ BC = 7/12 × 16.80

⇒ BC = 9.8

∴ The length of BC is 9.8 cm.

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