Ahhh, secants... not everyone's favorite, but mine!
The theorem suggests: multiplying the whole length of one secant by the external part of the secant, it is equal to the other side exterior secant x whole secant.
Knowing that, let's begin!
Let's use the total length of the first secant on a (x and 5).
5 + x * 5 =
and
4 + 6 * 6 =
BOTH of the equations must be equal...keep that in mind!
Let's set them into one full equation, shall we?
5 + x * 5 = 4 + 6 * 6
Simplify:
5 + 5x = 60
Now, we solve for X!
First, subtract 5 from both sides,
5 - 5 + 5x = 60 - 5
5x = 55
Divide 5 from both sides,
5x/5 = 55/5
x = 11!
Now, moving on to B.
5 + 3 * 3
&
x + 4 * 4
Same thing with the problem above, let's set them as one equation since they are equal to each other.
5 + 3 * 3 = x + 4 * 4
Simplify:
(It wouldn't be 4x + 4 because order of operations says to multiply 4 * 4 first! Just thought you should know...just in case.)
24 = 16 + x
Now, we subtract 16 from each side...
24 - 16 = 16 - 16 + x
Simplify:
8 = x
x= 8 for b!
Hope I could help you out!
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Have a good one.
God bless!
