Answer: 15 (choice B)
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Step-by-step explanation:
Triangle ABC is similar to triangle DEF.
The order of the letters is very important because the order tells us how the points match up.
- A pairs with D since they are the 1st letters
- B pairs with E since they are the 2nd letters
- C pairs with F since they are the 3rd letters
Those pairings then give these corresponding sides
- AB pairs with DE (both involve 1st and 2nd letters)
- BC pairs with EF (both involve 2nd and 3rd letters)
- AC pairs with DF (both involve 1st and 3rd letters)
We'll focus on the pairs AB & DE, as well as BC & EF. This is because they involve the variable x and also the values from the diagram.
The pair AB & DE forms the ratio AB/DE.
The pair BC & EF forms the ratio BC/EF.
Those ratios are equal when we have similar triangles like this.
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From here we have these steps:
AB/DE = BC/EF
x/6 = 10/4
4x = 6*10 ....... cross multiply
4x = 60
x = 60/4
x = 15
Therefore, choice B is the final answer.