64121=BC15.4the square root of 64 over 121 end-fraction end-root equals the fraction with numerator cap B cap C and denominator 15.4 end-fraction
811=BC15.48 over 11 end-fraction equals the fraction with numerator cap B cap C and denominator 15.4 end-fraction 4. Solve for side BCcap B cap C Multiply both sides by to isolate BCcap B cap C
64121=(BC15.4)264 over 121 end-fraction equals open paren the fraction with numerator cap B cap C and denominator 15.4 end-fraction close paren squared 3. Calculate the ratio of sides 64121=BC15
For two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides. This relationship is expressed by the formula:
Area(△ABC)Area(△DEF)=(BCEF)2the fraction with numerator Area open paren triangle cap A cap B cap C close paren and denominator Area open paren triangle cap D cap E cap F close paren end-fraction equals open paren the fraction with numerator cap B cap C and denominator cap E cap F end-fraction close paren squared 2. Substitute the known values Plug the given areas ( ) and the length of side EFcap E cap F ) into the formula: 64121=BC15
The length of side BCcap B cap C 1. Identify the relationship between areas and sides
Take the square root of both sides of the equation to find the ratio of the corresponding side lengths: 64121=BC15
BC=811×15.4cap B cap C equals 8 over 11 end-fraction cross 15.4 BC=8×1.4cap B cap C equals 8 cross 1.4 BC=11.2 cmcap B cap C equals 11.2 cm ✅ Final Answer The length of the corresponding side BCcap B cap C