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: The length of side BCcap B cap C 1
import math area_abc = 64 area_def = 121 ef = 15.4 # Ratio of areas of similar triangles is equal to the square of the ratio of their corresponding sides. # (BC / EF)^2 = Area(ABC) / Area(DEF) # BC / EF = sqrt(Area(ABC) / Area(DEF)) bc = ef * math.sqrt(area_abc / area_def) print(f"{bc=}") Use code with caution. Copied to clipboard The length of side BCcap B cap C 1
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: The length of side BCcap B cap C 1
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