Question

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

Answer 1

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