Answer:
x = 10
Step-by-step explanation:
Use CPCTC (Corresponding parts of congruent triangles are congruent).
Set the ratios:
[tex]\frac{6.5}{5} = \frac{6.5 + 6.5}{x}[/tex]
First, simplify. Combine like terms:
[tex]\frac{6.5}{5} = \frac{13}{x}[/tex]
Next, cross multiply.
[tex]5 * x * \frac{6.5}{5} = \frac{13}{x} * x * 5\\x * 6.5 = 13 * 5\\6.5x = 65\\[/tex]
Isolate the variable, x. Divide 6.5 from both sides of the equation:
[tex]\frac{(6.5x)}{6.5} = \frac{(65)}{6.5} \\\\x = \frac{65}{6.5}\\x = 10[/tex]
Check:
[tex]\frac{5}{6.5} = \frac{x}{13}[/tex]
Plug in 10 for x (Your answer). Cross multiply, then simplify:
[tex]\frac{5}{6.5} = \frac{10}{13}[/tex]
[tex]13 * 6.5 * \frac{5}{6.5} = \frac{10}{13} * 13 * 6.5[/tex]
[tex]13 * 5 = 10 * 6.5[/tex]
[tex]65 = 65[/tex] (True).
~
