Answer:
x = 4.00
Explanation:
You want the value of x when CA=3x, AB=20, BE=16, ED=24 in the triangle in the diagram.
Proportion
We see that length BD is 16+24 = 40, which is twice the length BA = 20. This means the segments of BD are twice the length of the corresponding segments of BA.
CA = 3x = (1/2)ED
3x = 1/2(24) = 12
x = 4 . . . . . . divide by 3
The value of x is 4.00.
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Additional comment
Triangle BAD is similar to triangle BCE, so corresponding sides are proportional. This also means corresponding segments of sides are proportional.
We know the triangles are similar by the AA similarity postulate. Corresponding angles are congruent where a transversal crosses parallel lines, and angle B is congruent to itself.
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