Question

formal proofs online practice
complete this assessment to review what youve learned. it will not count toward your grade.
use the image to answer the question
if ( bc = 3x + 15 ), ( ef = 4x + 4 ), and ( ad = 6x - 34 ), find ( ad )
(1 point)
( ad=square )

Explanation:

Step1: Apply the mid - segment theorem

The mid - segment theorem for trapezoids states that \(EF=\frac{BC + AD}{2}\).

Step2: Substitute the given expressions

Substitute \(BC = 3x + 15\), \(EF = 4x + 4\), and \(AD = 6x-34\) into the formula \(4x + 4=\frac{(3x + 15)+(6x - 34)}{2}\).

Step3: Solve the equation for \(x\)

First, simplify the right - hand side: \(\frac{(3x + 15)+(6x - 34)}{2}=\frac{9x-19}{2}\).
The equation becomes \(2(4x + 4)=9x - 19\).
Expand the left - hand side: \(8x+8 = 9x - 19\).
Subtract \(8x\) from both sides: \(8=x - 19\).
Add \(19\) to both sides: \(x=27\).

Step4: Find the value of \(AD\)

Substitute \(x = 27\) into \(AD = 6x-34\).
\(AD=6\times27-34\).
\(AD = 162-34\).
\(AD = 110\).

Answer:

\(AD = 110\)