AB ≅ CD. Find the length of BD.?

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SUMMARY

The problem states that segments AB and CD are congruent, leading to the equation 7x + 7 = 8x + 3. Solving for x yields x = 4. Substituting x back into the expression for BD, calculated as 3x - 4, results in a length of 8. The correct answer is A) 8.

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Homework Statement



AB ≅ CD. Find the length of BD.?

img42.gif


AB ≅ CD. Find the length of BD.


Homework Equations




A) 8
B) 10
C) 4
D) 7
E) -7



The Attempt at a Solution




AB = 2x + 5x + 7 = 7x + 7

CD = 5x + 7 + 3x - 4 = 8x + 3

AB ~= CD
7x + 7 = 8x + 3

7 - 3 = 8x - 7x => x = 4

BD = 3x - 4 = 3(4) - 4 = 8

ans: A) 8
 
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