Question

5.1 assignment
3 of 22
possible points: 0.45
algebra find the length of \\( \overline{ab} \\).
diagram of a rhombus or kite with vertices b, e, c, a; d is the intersection of the diagonals, with bd and dc marked as equal, and angle at d is a right angle. lengths: ab is \\( 9x + 1 \\), ac segment (or another side) is \\( 7x + 13 \\)
\\( ab = \\) blank units

Explanation:

Step1: Set up the equation

Since \(AB = AC\) (they are equal in the geometric figure), we have \(9x + 1=7x + 13\).

Step2: Solve for \(x\)

Subtract \(7x\) from both sides: \(9x-7x + 1=7x-7x + 13\), which simplifies to \(2x+1 = 13\).
Subtract \(1\) from both sides: \(2x+1 - 1=13 - 1\), so \(2x=12\).
Divide both sides by \(2\): \(x=\frac{12}{2}=6\).

Step3: Find the length of \(AB\)

Substitute \(x = 6\) into the expression for \(AB\) (\(AB=9x + 1\)).
\(AB=9\times6+1=54 + 1=55\).

Answer:

\(55\)