Answer:
DB=26 units
Explanation:
In rectangle ABCD
• AC=7x-2
,
• DE = 3x+1
The diagonals of a rectangle are equal and bisect each other.
Thus, it implies that:
[tex]DE=\frac{1}{2}AC[/tex]
Substituting the given values:
[tex]\begin{gathered} 3x+1=\frac{1}{2}(7x-2) \\ 2(3x+1)=7x-2 \\ 6x+2=7x-2 \\ 2+2=7x-6x \\ x=4 \end{gathered}[/tex]
Since the diagonals are equal:
[tex]\begin{gathered} DB=AC \\ AC=7x-2 \\ =7(4)-2 \\ =28-2 \\ =26\text{ units} \\ \implies DB=26\text{ units} \end{gathered}[/tex]
The length of DB is 26 units.
