triangle help plz

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triangle help plz

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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|dw:1439402369884:dw| Given that:AB-8 BC=3 DE=13 BD=x What is the value of xx?

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I'd say just set up a ratio between the corresponding sides of the triangle and use substitution to find the value of x, then multiply x by itself.
ok imma be real with u but i only got x part and multiply it now slow down and explain
If you'll notice, since triangle ABC and triangle ADE both share point A, they are similar triangles. This means that we can set up a proportion between sides AB and AD, and sides BC and DE.
It would look like this, \[\frac{ AB }{ AD } = \frac{ BC }{ DE }\] This is a proportion between the side lengths of the smaller and larger triangles. Now all you have to do is substitute to find the value of x. I'll explain further.
Since AB is 8, we would substitute that value in for the proportion. This continues with the other values until we arrive at... \[\frac{ 8 }{ 8 + x } = \frac{ 3 }{ 13 }\] All you have to do now is cross multiply and you'll be able to find the value of x.
wht pellet im fried im lost again ahhhhhhhh my brain
@jamesr Where have you been able to follow up to?
the part where it would look like ...
Are you talking about the proportion I set up? The second proportion I set up is the same as the first one. All I did was substitute in values. In simpler terms, if we're trying to find... \[\frac{ AB }{ AE } = \frac{ BC }{ DE }\] This proportion is the exact same as... \[\frac{ 8 }{ 8 + x } = \frac{ 3 }{ 13 }\] The only thing the second proportion is doing is substituting in the values of AB, AE, BC, and DE.

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