Ex.6.4 Q1 Triangles Solution - NCERT Maths Class 10

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Let \(\Delta ABC \sim \Delta DEF\) 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 \(BC. \)


 Video Solution
Ex 6.4 | Question 1

Text Solution


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.


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

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

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