The corresponding sides of two similar triangles ABC and DEF are BC = 9.1cm and EF = 6.5cm. If the rerimeter of $\triangle\text{DEF}$ is 25cm, find the perimeter of $\triangle\text{ABC}.$
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$\triangle\text{ABC}$ and $\triangle\text{DEF}$ are two similar triangles, therefore corresponding sides of both the triangle are proportional.
Hence, $\frac{\text{Perimeter of }\triangle\text{ABC}}{\text{Perimeter of }\triangle\text{DEF}}=\frac{\text{BC}}{\text{EF}}$
Let peremeter of $\triangle\text{ABC}=\text{x} \text{ cm}$
$\therefore\frac{\text{x}}{25}=\frac{9.1}{6.5}$
$\text{x}=\frac{9.1\times25}{6.5}=35\text{cm}$
Hence, perimeter of $\triangle\text{ABC}=35\text{ cm}$
Hence, $\frac{\text{Perimeter of }\triangle\text{ABC}}{\text{Perimeter of }\triangle\text{DEF}}=\frac{\text{BC}}{\text{EF}}$
Let peremeter of $\triangle\text{ABC}=\text{x} \text{ cm}$
$\therefore\frac{\text{x}}{25}=\frac{9.1}{6.5}$
$\text{x}=\frac{9.1\times25}{6.5}=35\text{cm}$
Hence, perimeter of $\triangle\text{ABC}=35\text{ cm}$
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