Question

ABC is similar to DEF. The measure of AB = 6, the measure of DE = 18, the measure of BC = 12, and the measure of DF = 15.Find the measures of AC and EF.

Answer 1

Step 1:

In this question, we are given the following:

ABC is similar to DEF.

The measure of AB = 6,

the measure of DE = 18,

the measure of BC = 12,

and the measure of DF = 15.

Find the measures of AC and EF.​

Step 2:

The details of the solution are as follows:

`and\text{ AB = 6, DE = 18, BC = 12, DF = 15}`
`\frac{}{}(6)/(18)=(12)/(EF)=(AC)/(15)`
`\begin{gathered} cross-multiply,\text{ we have that:} \\ \text{6 }*\text{ EF =18 }*\text{ 12} \\ Divide\text{ both sides by 6, we have that:} \\ EF\text{ =}(18*12)/(6)=(216)/(6)=\text{ 36} \\ Hence,\text{ EF = 36} \end{gathered}`
`\begin{gathered} (6)/(18)=(AC)/(15) \\ cross-multiply\text{ we have that:} \\ 6*15\text{ = AC }*18 \\ Divide\text{ both sides by 18, we have that:} \\ AC\text{ =}\frac{6\text{ }*15}{18}=(90)/(18)=\text{ 5} \\ Hence,\text{ AC = 5} \end{gathered}`