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Triangles — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsTriangles3 Marks
Question
If $\triangle\text{ABC}$ and $\triangle\text{DEF}$ are two triangles such that $\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{CA}}{\text{FD}}=\frac{3}{4},$ then write $\text{Area}(\triangle\text{ABC}):\text{Area}(\triangle\text{DEF.})$
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Answer

In two $\triangle\text{s}$ ABC and DEF
$\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{CA}}{\text{FD}}=\frac{3}{4}$
$\therefore\triangle\text{ABC}\sim\triangle\text{DEF}$ (Sides of two similar triangles are proportional)
$\therefore\frac{\text{area}(\triangle\text{ABC})}{\text{area}(\triangle\text{DEF})}=\frac{\text{AB}^2}{\text{DE}^2}=\frac{(3)^2}{(4)^2}=\frac{9}{16}$
$\text{area}(\triangle\text{ABC}):\text{area}(\triangle\text{DEF})=9:16$

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