If ∆ ABC ~ ∆ DEF, BC = 12 cm, EF = 10 cm, and AC = 18 cm, find DF.
by ratios
DF/10 = 18/12
solve for DF
To find the length of DF, we can use the property of similar triangles which states that corresponding sides of similar triangles are proportional to each other.
In this case, we know that ∆ ABC is similar to ∆ DEF. This means that the ratio of the length of corresponding sides in the two triangles should be equal.
Let's denote the length of DF as x.
According to the proportionality of sides, we can set up the following equation:
BC/EF = AC/DF
Substituting the given values, we have:
12/10 = 18/x
To solve for x, we can cross multiply and solve for x:
12x = 10 * 18
12x = 180
x = 180/12
x = 15
Therefore, the length of DF is 15 cm.