Question

△ABC∼△DEF, the area of △ABC=9 cm² and the area of △DEF = 16 cm². If BC=2.1 cm, then EF=

• A. 2.8 cm
• B. 4.2 cm
• C. 2.5 cm
• D. 4.1 cm

Answer 1

The Correct Option is A

$BC = 2.1$ cm, not $BC = 2:1$. Using the formula $\frac{A_{ABC}}{A_{DEF}} = (\frac{BC}{EF})^2$, we have $$ \frac{9}{16} = \left( \frac{2.1}{EF} \right)^2 $$ Taking the square root of both sides, $$ \frac{3}{4} = \frac{2.1}{EF} $$ $$ EF = \frac{4 \times 2.1}{3} = \frac{8.4}{3} = 2.8 $$ So, $EF = 2.8$ cm.