For two similar triangles ABC and DEF, the scale factor of ∆ABC to ∆DEF is 2 : 3. If AB = 2(BC) and DE = 3(BC), what is EF?
reverse the ratio. DEF:ABC = 3:2
EF = 3/2 BC
To find the length of EF, we need to determine the relationship between the sides of the two triangles.
Given that the scale factor of ∆ABC to ∆DEF is 2:3, this means that for every 2 units of length in triangle ABC, there are 3 units of length in triangle DEF.
Since AB = 2(BC), we can let BC be the base unit of measurement. Therefore, AB = 2(1)BC = 2BC and DE = 3(1)BC = 3BC.
Next, we can set up a proportion using the respective sides of the triangles:
AB/DE = BC/EF
Substituting the values we have:
2BC/3BC = BC/EF
Cross multiply:
2BC * EF = 3BC * BC
Cancel out the BC terms:
2EF = 3BC
Finally, solve for EF:
EF = (3/2)BC
Since we set BC as the base unit of measurement, BC = 1. Therefore:
EF = (3/2)(1) = 3/2 = 1.5
So, the length of EF is 1.5 units.