Question

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

Answer 1

The Solution.

The ratios are

$\frac{6}{10}=\frac{12}{20}=\frac{4x+2}{4x+9}$

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

$\frac{6}{10}=\frac{4x+2}{4x+9}$

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

$x=\frac{34}{16}=\frac{17}{8}\text{ or 2}\frac{1}{8}$

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

Hence, the correct answers are;

x = 17/8

AC = 10.5

DF = 17.5