Question

if the length of ( overline{be} ) is ( 2x + 1 ) and the length of ( overline{cd} ) is ( 7x - 25 ), what is the length of ( overline{be} )? your answer should be a number and not contain any variables.

Explanation:

Step1: Identify BE and CD relationship

From the diagram, \( BE \) is a midline (since segments are marked congruent), so \( BE=\frac{1}{2}CD \) (midline theorem: midline of a triangle is half the length of the third side). So set \( 2x + 1=\frac{1}{2}(7x - 25) \).

Step2: Solve for x

Multiply both sides by 2: \( 2(2x + 1)=7x - 25 \)
Simplify: \( 4x + 2 = 7x - 25 \)
Subtract \( 4x \): \( 2 = 3x - 25 \)
Add 25: \( 27 = 3x \)
Divide by 3: \( x = 9 \)

Step3: Find length of BE

Substitute \( x = 9 \) into \( BE = 2x + 1 \): \( BE = 2(9)+1 = 18 + 1 = 19 \)

Answer:

19