Question

Answer below due to inability to type out the following question.

Answer 1

`11.04\text{ or }(-2+√(580))/(2)`

Step-by-step explanation

Given that:

In the figure provided, the triangle EFG is similar to the triangle is ECD

FE = 12

CD = 12

FG = CF + 2

To find the length CF, apply the similarity triangle theorem

`\frac{\text{ FE}}{\text{ CF}}\text{ }=\frac{\text{ FG}}{CD}`

Substitute the given data into the above equation

`\begin{gathered} \text{ }(12)/(CF)=(CF+2)/(12) \\ \text{ cross multiply} \\ \text{ 12}*12\text{ }=\text{ CF\lparen CF + 2\rparen} \\ \text{ 144 }=\text{ CF}^2\text{ }+\text{ 2CF} \\ CF^2\text{ }+\text{ 2CF -144 =0} \\ \text{ Find CF using the general formula} \\ x\text{ }=\text{ }\frac{-b\pm\sqrt{b^2-\text{ 4ac}}}{\placeholder{⬚}} \\ \text{ a }=1,\text{ b}=2,\text{ c}=-144 \\ \text{ x }=\frac{-2\text{ }\pm√(2^2-4*1*(-144))}{2} \\ \text{ x}=\text{ }(-2\pm√(4+576))/(2) \\ \text{ x }=\text{ }(-2\pm√(580))/(2) \\ \text{ x }=\text{ }(-2+√(580))/(2) \\ \text{ x }=\text{ }(-2+24.083)/(2) \\ \text{ x }=(22.083)/(2) \\ \text{ x }=11.04 \\ \text{ Therefore, CF is 11.04 or }(-2+√(580))/(2) \end{gathered}`