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Given △BAD AB = 3x - 4 ED = 24 CA = 12 BE = 3x Find x to the nearest hundredth.

Given BAD AB 3x 4 ED 24 CA 12 BE 3x Find X To The Nearest Hundredth class=

Sagot :

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Answer:

  x = 10.67

Step-by-step explanation:

The triangles shown are similar, so corresponding sides are proportional. This lets us write a relation that can be solved for x.

Setup

For the given figure, we can write the proportion ...

  AB/CA = DB/ED . . . . . . where DB = ED +BE

  (3x-4)/12 = (24 +3x)/24 . . . . . . substitute given values

Solution

Multiplying by 24 gives ...

  2(3x -4) = 3x +24

  6x -8 = 3x +24 . . . . . eliminate parentheses

  3x = 32 . . . . . . . . add 8-3x

  x = 32/3 = 10 2/3 ≈ 10.67 . . . . . divide by 3 and convert to decimal

The value of x to the nearest hundredth is 10.67.

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