Question

question 6
find ( x ) and then ( overline{a b} ) and ( overline{b c} ).
note: always make sure the value of ( x ) produces positive lengths.
( x=)
( overline{a b}=)
( overline{b c}=)

Explanation:

Step1: Set up the equation

Since \(AB = BC\) (the triangle is isosceles as \(AC\) is marked as having equal segments), we have \(7x + 6=8x + 1\).

Step2: Solve for \(x\)

Subtract \(7x\) from both sides: \(6=x + 1\).
Then subtract \(1\) from both sides: \(x=6 - 1=5\).

Step3: Find \(AB\)

Substitute \(x = 5\) into \(AB=7x + 6\). So \(AB=7\times5+6=35 + 6=41\).

Step4: Find \(BC\)

Substitute \(x = 5\) into \(BC=8x + 1\). So \(BC=8\times5+1=40 + 1=41\).

Answer:

\(x = 5\), \(\overline{AB}=41\), \(\overline{BC}=41\)