Question

Given SUP ~ MAN. If SU=20, MA=15, UP=x, and AN=2x-7, then AN equals... Round answer to the nearest tenth.

Answer 1

Answer:

$AN=4.2$

Step-by-step explanation:

If SUP is congruent to MAN, then we can solve this situation by proportional relationships or similar triangles:

$\begin{gathered} \frac{SU}{MA}=\frac{UP}{AN} \\ \frac{20}{15}=\frac{x}{2x-7} \end{gathered}$

Then, solve for x:

$\begin{gathered} 20(2x-7)=15x \\ 40x-140=15x \\ 40x-15x=140 \\ 25x=140 \\ x=\frac{140}{25} \\ x=5.6 \end{gathered}$

Now, having the value of x, we can substitute into the expression for AN:

$\begin{gathered} AN=2(5.6)-7 \\ AN=4.2 \end{gathered}$