Mathematics: In the diagram, AB =BC,AC = CD, and AD 12. Find the lengths of all segments in the diagram. Suppose you choose one of the segments at random. What is the probability that the measure of the segment is greater than 3? Explain your reasoning.

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In the diagram, AB =BC,AC = CD, and AD 12. Find

mkeyes83

01.02.2022

Probability that the measure of a segment is greater than 3 = 0.6

Step-by-step explanation:

From the given attachment,

AB ≅ BC, AC ≅ CD and AD = 12

Therefore, AC ≅ CD = $\frac{1}{2}(\text{AD})$

= 6 units

Since AC ≅ CD

AB + BC ≅ CD

2(AB) = 6

AB = 3 units

Now we have measurements of the segments as,

AB = BC = 3 units

AC = CD = 6 units

AD = 12 units

Total number of segments = 5

Length of segments more than 3 = 3

Probability to pick a segment measuring greater than 3,

= $\frac{\text{Total number of segments measuring greater than 3}}{Total number of segments}$

= $\frac{3}{5}$

= 0.6

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