The following is true about similar triangles ABC and DEF.
ABDE=BCEF=ACDF=21
Which could be the lengths of BC¯¯¯¯¯ and EF¯¯¯¯¯?
f BC=3 and EF=9
g BC=6 and EF=3
h BC=9 and EF=3
j BC=3 and EF=6
To determine the lengths of BC¯¯¯¯¯ and EF¯¯¯¯¯, we need to consider the ratios of corresponding sides in similar triangles. According to the given information, ABDE=BCEF=ACDF=21.
Let's analyze the options:
Option f: BC=3 and EF=9
The ratio of ABDE to BC¯¯¯¯¯ is 21/3 = 7, and the ratio of DEF to EF¯¯¯¯¯ is 21/9 = 7/3. Therefore, this option does not satisfy the condition that corresponding sides have the same ratio.
Option g: BC=6 and EF=3
The ratio of ABDE to BC¯¯¯¯¯ is 21/6 = 7/2, and the ratio of DEF to EF¯¯¯¯¯ is 21/3 = 7. Therefore, this option satisfies the condition that corresponding sides have the same ratio.
Option h: BC=9 and EF=3
The ratio of ABDE to BC¯¯¯¯¯ is 21/9 = 7/3, and the ratio of DEF to EF¯¯¯¯¯ is 21/3 = 7. Therefore, this option satisfies the condition that corresponding sides have the same ratio.
Option j: BC=3 and EF=6
The ratio of ABDE to BC¯¯¯¯¯ is 21/3 = 7, and the ratio of DEF to EF¯¯¯¯¯ is 21/6 = 7/2. Therefore, this option does not satisfy the condition that corresponding sides have the same ratio.
Based on the analysis, options g and h are possible lengths for BC¯¯¯¯¯ and EF¯¯¯¯¯.