, ar( )=9cm^2, ar( )=16cm^2. If BC = 2.1 cm, then the measure of … - Vidyadip

MCQ

$\triangle\text{ABC}\sim\triangle\text{DEF},$
$\text{ar}(\triangle\text{ABC})=9\text{cm}^2,\ \text{ar}(\triangle\text{DEF})=16\text{cm}^2.$ If $\text{BC} = 2.1\ cm,$ then the measure of $\text{EF}$ is:

✓
$2.8\ cm.$
B
$4.2\ cm.$
C
$2.5\ cm.$
D
$4.1\ cm.$

✓

Answer

Correct option: A.

$2.8\ cm.$

Given: $\text{Ar}(\triangle\text{ABC})=9\text{cm}^2,$
$\text{Ar}(\triangle\text{DEF})=16\text{cm}^2,$ and $\text{BC}=2.1\text{cm}$
To find: measure of $\text{EF}$
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
$\frac{\text{Ar}(\triangle\text{ABC})}{\text{Ar}(\triangle\text{DEF})}=\frac{\text{BC}^2}{\text{EF}^2}$
$\frac{9}{16}=\frac{2.1^2}{\text{EF}^2}$
$\frac{3}{4}=\frac{2.1}{\text{EF}}$
$\text{EF}=2.8\text{cm}$
Hence the correct answer is $A.$

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