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Triangle ABC is congruent to triangle DEF. If DE = 41, EF = 23, DF = 36, and AC = 5x − 9, what is x? Round to the nearest tenth. a6.4 b9.0 c9.4 d10.0

Sagot :

Lets draw a picture of the problem:

Since both triangles are congruent, this means that

[tex]\begin{gathered} AB=DE=41 \\ BC=EF=23 \end{gathered}[/tex]

and

[tex]AC=DF[/tex]

which means that

[tex]5x-9=36[/tex]

So, by adding 9 to both side, we have

[tex]5x=45[/tex]

and by dividing both sides by 5, we obtain

[tex]\begin{gathered} x=\frac{45}{5} \\ x=9 \end{gathered}[/tex]

Therefore, the answer is option b

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