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,

$\Rightarrow\frac{x}{5}=\frac{y}{12}=\frac{26}{3}$

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.

$\Rightarrow\frac{x}{5}=\frac{26}{3}$

Solving for x,

$\begin{gathered} \Rightarrow x=\frac{26\cdot5}{3}=43.333\ldots \\ \Rightarrow AB=43.333\ldots \end{gathered}$

Similarly, solving for y,

$\begin{gathered} \Rightarrow\frac{y}{12}=\frac{26}{3} \\ \Rightarrow y=26\cdot\frac{12}{3}=104 \\ \Rightarrow BC=104 \end{gathered}$