Ex.6.4 Q1 Triangles Solution - NCERT Maths Class 10

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Question

Let \(\Delta {\rm{ }}ABC{\rm{ }}\sim{\rm{ }}\Delta DEF\) and their areas be, respectively, \({64\,\rm{c}}{{\rm{m}}^{\rm{2}}}\) and \({121\,\rm{c}}{{\rm{m}}^{\rm{2}}}\). If \(E F=15.4\, \rm{cm}\) find \(BC. \)

Diagram

Text Solution

 

Reasoning:

As we know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Steps:

\(\Delta ABC \sim \Delta DEF\)

\[\begin{aligned} \frac{\text { Area of } \Delta A B C}{\text { Area of } \Delta D E F} &=\frac{(B C)^{2}}{(E F)^{2}} \\ \\ \frac{64\, \rm{c m^{2}}}{121\, \rm{c m^{2}}} &=\frac{(B C)^{2}}{(15.4)^{2}} \\(B C)^{2} &=\frac{(15.4)^{2} \times 64}{121} \\ B C &=\frac{15.4 \times 8}{11} \\ B C &=11.2\, \mathrm{cm} \end{aligned}\]

  
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