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Triangles — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsTriangles2 Marks
Question
Triangle ABC and DEF are similar.
If area $\big(\triangle\text{ABC}\big) = 9\text{cm}^2,$ area $\big(\triangle\text{DEF}\big) = 64\text{cm}^2$ and DE = 5.1cm, find AB.
✓

Answer

$\because\triangle\text{ABC}\sim\triangle\text{DEF},$
$\therefore\frac{\text{area}(\triangle\text{ABC)}}{\text{area}(\triangle\text{DEF)}}=\frac{\text{AB}^2}{\text{DE}^2}$
$\Rightarrow\frac{9}{64}=\frac{\text{AB}^2}{(5.1)^2}\Rightarrow\frac{(3)^2}{(8)^2}=\frac{\text{AB}^2}{(5.1)^2)}$
$\Rightarrow\frac{3}{8}=\frac{\text{AB}}{5.1}\Rightarrow\text{AB}=\frac{3\times5.1}{8}=\frac{15.3}{8}$
$\therefore\text{AB}=1.9125$

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