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Triangle ABC is similar to triangle DEF. The following ratios of corresponding sides are equal,

User Spoko
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The Solution.

The ratios are


(6)/(10)=(12)/(20)=(4x+2)/(4x+9)

To find the value of x, we shall solve the equation below:


(6)/(10)=(4x+2)/(4x+9)

Cross multiplying, we get


6(4x+9)=10(4x+2)

Clearing the brackets, we get


24x+54=40x+20

Collecting the like terms, we get


\begin{gathered} 54-20=40x-24x \\ 34=16x \end{gathered}

Dividing both sides by 16, we get


x=(34)/(16)=(17)/(8)\text{ or 2}(1)/(8)

So, the value of x is 17/8 or 2 1/8

To find AC and DF, we shall substitute 17/8 for x in the expression that defines AC and DF.


\begin{gathered} AC=4x+2=4((17)/(8))+2 \\ \\ AC=(17)/(2)+2=8.5+2=10.5 \end{gathered}
\begin{gathered} DF=4x+9=4((17)/(8))+9 \\ \\ DF=(17)/(2)+9=8.5+9=17.5 \end{gathered}

Hence, the correct answers are;

x = 17/8

AC = 10.5

DF = 17.5

User Raja Anbazhagan
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