Let О”abcв€јо”def And Their Areas Be Respectively 64cmві And 121cmві. If Ef=15.4cm Find Bc. · No Sign-up

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:

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. Identify the relationship between areas and sides This relationship is expressed by the formula: 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:

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 Copied to clipboard 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

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 This relationship is expressed by the formula: 811=BC15

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