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
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: 811=BC15
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 Calculate the ratio of sides Take the square
Take the square root of both sides of the equation to find the ratio of the corresponding side lengths: 811=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:
The length of side BCcap B cap C 1. Identify the relationship between areas and sides