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Triangles — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsTriangles2 Marks
Question
Triangle ABC and DEF are similar.
If area $\big(\triangle\text{ABC}\big) =16\text{cm}^2,$ area $\big(\triangle\text{DEF}\big) =25\text{cm}^2 $ and BC = 2.3cm, find EF.
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Answer

$\because\triangle\text{ABC}\sim\triangle\text{DEF},$
$\therefore\frac{\text{area}(\triangle\text{ABC)}}{\text{area}(\triangle\text{DEF)}}=\frac{\text{BC}^2}{\text{EF}^2}$

$\Rightarrow\frac{16}{25}=\frac{(2.3)^2}{\text{EF}^2}\Rightarrow\frac{(4)^2}{(5)^2}=\frac{(2.3)^2}{\text{EF}^2}$
$\Rightarrow\frac{4}{5}=\frac{2.3}{\text{EF}}\Rightarrow\text{EF}=\frac{2.3\times5}{4}$
$\therefore\text{EF}=\frac{11.5}{4}=2.875\text{cm}$

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