Ex.6.4 Q1 Triangles Solution - NCERT Maths Class 10

Go back to  'Ex.6.4'


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 \(BC. \)


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.


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

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

Learn math from the experts and clarify doubts instantly

  • Instant doubt clearing (live one on one)
  • Learn from India’s best math teachers
  • Completely personalized curriculum