Question

I know how to get perimeter ratios and set up proportions but I get lost in the process.Find the value of x

Answer 1

Case: Simiar traiagles

Method:

It is good practice to separate the triangles into the two identifiable similar triangles

Using similar angle scale ratio:

`\begin{gathered} (13)/(x+3)=(13+x)/(x+19) \\ 13(x+19)=(x+3)(13+x) \\ 13x+247=13x+x^2+39+3x \\ x^2+3x+13x-13x+39-_247=0 \\ x^2+3x-208=0 \\ Solving\text{ }the\text{ }quadratics \\ x=13\text{ }or\text{ }x=-16 \end{gathered}`

x cannot be -16 because no sides can have negative magnitudes

Hence, x can only be 13.

Final answer:

x= 13