Triangle ABC is similar to triangle DEF. The length of AC is 12 cm. The length of BC is 18 cm. The length of DF is 10 cm. What is the length of EF?
Mathematics · Middle School · Sun Jan 24 2021
Answered on
To solve this problem, we need to use the concept of similar triangles. When two triangles are similar, the ratios of the lengths of their corresponding sides are equal.
Given that triangle ABC is similar to triangle DEF, we can write the ratio of the corresponding sides AC to DF and BC to EF as equal to each other.
So, the ratio AC/DF is equal to BC/EF.
Now, plug in the known lengths:
AC/DF = BC/EF 12/10 = 18/EF
To find EF, we cross-multiply:
12 * EF = 10 * 18 EF = (10 * 18) / 12 EF = 180 / 12 EF = 15
So, the length of EF is 15 cm.