Question

Find the length of x. help please !

Answer 1

x = 10

Explanation:

Use CPCTC (Corresponding parts of congruent triangles are congruent).

Set the ratios:

`(6.5)/(5) = (6.5 + 6.5)/(x)`

First, simplify. Combine like terms:

`(6.5)/(5) = (13)/(x)`

Next, cross multiply.

`5 * x * (6.5)/(5) = (13)/(x) * x * 5\\x * 6.5 = 13 * 5\\6.5x = 65\\`

Isolate the variable, x. Divide 6.5 from both sides of the equation:

`((6.5x))/(6.5) = ((65))/(6.5) \\\\x = (65)/(6.5)\\x = 10`

Check:

`(5)/(6.5) = (x)/(13)`

Plug in 10 for x (Your answer). Cross multiply, then simplify:

`(5)/(6.5) = (10)/(13)`

`13 * 6.5 * (5)/(6.5) = (10)/(13) * 13 * 6.5`

`13 * 5 = 10 * 6.5`

`65 = 65` (True).

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