Explanation:
The diagonals of a rectangle are congruent and the intersecting point is the middle point of both:
Therefore, for this problem DZ ≅ BZ and DB = DZ + BZ. Also DB ≅ AC. Since DZ ≅ BZ
[tex]\begin{gathered} AC=2DZ \\ 5x+3=x+6 \end{gathered}[/tex]
Solving for x:
[tex]\begin{gathered} 5x-x=6-3 \\ 4x=3 \\ x=\frac{3}{4} \end{gathered}[/tex]
To find AC we just have to replace x = 3/4 into the expression for its length:
[tex]\begin{gathered} AC=5x+3 \\ AC=5\cdot\frac{3}{4}+3=\frac{27}{4}=6.75 \end{gathered}[/tex]
Answer:
AC = 6.75
