Question

Please help! This is Geometry I don't know what to do

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Answer 1

`\huge\boxed{x=6}`

Explanation:

`\triangle ABC\ \text{and}\ \triangle ADB\ \text{are similar (AA). Therefore corresponding sides are in proportion.}\\\\(BD)/(BC)=(AB)/(AC)\\\\\text{We have}\\\\BD=x\\BC=10\\AB=7.5\\AC=12.5\\\\\text{Subtitute:}\\\\(x)/(10)=(7.5)/(12.5)\\\\(x)/(10)=(7.5\cdot10)/(12.5\cdot10)\\\\(x)/(10)=(75:25)/(125:25)\\\\(x)/(10)=(3)/(5)\qquad|\text{cross multiply}\\\\(5)(x)=(3)(10)\\\\5x=30\qquad|\text{divide both sides by 5}\\\\(5x)/(5)=(30)/(5)\\\\x=6`