Question

Can someone please help me find the valu of X?

Answer 1

The midsegment determines a smaller triangle that is similar to the larger triangle. If two triangles are similar, then their side lengths are at the same ratio, so that:

`\begin{gathered} (5x)/(45)=(20)/(20+16) \\ (5x)/(45)=(20)/(36) \end{gathered}`

From this expression, you can determine the value of x:

-First. multiply both sides by 45:

`\begin{gathered} 45((5x)/(45))=45((20)/(36)) \\ 5x=25 \end{gathered}`

-Second, divide both sides by 5 to determine the value of x:

`\begin{gathered} (5x)/(5)=(25)/(5) \\ x=5 \end{gathered}`

The value of x is equal to 5