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

`AN=4.2`

Explanation:

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

`\begin{gathered} (SU)/(MA)=(UP)/(AN) \\ (20)/(15)=(x)/(2x-7) \end{gathered}`

Then, solve for x:

`\begin{gathered} 20(2x-7)=15x \\ 40x-140=15x \\ 40x-15x=140 \\ 25x=140 \\ x=(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}`