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3 years ago

SegmentAB≅SegmentCD. AC = 6x-12 , BC = 4, and CD = 3x-2. Find AB and CD. (Geometry Proof)

Mathematics

1 answer:

mote1985 [20]3 years ago

3 0

Answer/Step-by-step explanation:

Given:

AC = 6x - 12

BC = 4

CD = 3x - 2

Required:

Determine length of AB and CD.

SOLUTION:

AC - BC = AB

(6x - 12) - 4 = AB (Substitution)

6x - 12 - 4 = AB

6x - 16 = AB

Since AB ≅ CD, therefore,

AB = CD

6x - 16 = 3x - 2 (Substitution)

Combine like terms

6x - 3x = 16 - 2

3x = 14

Divide both sides by 3

x = 4.7

Find AB

6x - 16 = AB

Plug in the value of x

6(4.7) - 16 = AB

28.2 - 16 = AB

12.2 = AB

Find CD

CD = 3x - 2

Plug in the value of x

CD = 3(4.7) - 2

CD = 14.1 - 2

CD = 12.1

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