Question

I have a test an in hour and I need help with what to do

Answer 1

Suppose that triangles ABC and DFE are similar. Therefore, the ratio between their corresponding sides is constant. Let x and y be

`\begin{gathered} AB=x \\ BC=y \end{gathered}`

Then,

`\Rightarrow(x)/(5)=(y)/(12)=(26)/(3)`

Triangle DFE is impossible, the lengths of its sides are impossible to construct in such a manner that the result is a right triangle whose hypotenuse is 3. DFE is an impossible triangle, the hypotenuse of a right triangle is always its largest side.

However, we can algebraically find x and y, although it would not make any sense geometrically speaking.

`\Rightarrow(x)/(5)=(26)/(3)`

Solving for x,

`\begin{gathered} \Rightarrow x=(26\cdot5)/(3)=43.333\ldots \\ \Rightarrow AB=43.333\ldots \end{gathered}`

Similarly, solving for y,

`\begin{gathered} \Rightarrow(y)/(12)=(26)/(3) \\ \Rightarrow y=26\cdot(12)/(3)=104 \\ \Rightarrow BC=104 \end{gathered}`