Answer:
[tex]AB= \frac{97}{3}[/tex]
Step-by-step explanation:
Properties of Rhombus
- All sides of the rhombus are equal.
- The opposite sides of a rhombus are parallel.
- Opposite angles of a rhombus are equal.
- In a rhombus, diagonals bisect each other at right angles.
- Diagonals bisect the angles of a rhombus.
We are given two sides of the rhombus BC and CD. According to the first property:
4x + 15 = 7x + 2
Subtracting 4x:
15 = 3x + 2
Subtracting 2:
13 = 3x
Dividing by 3:
[tex]x=\frac{13}{3}[/tex]
It's required to find the side AB. Applying the first property again:
AB= BC = CD = 4x + 15
[tex]AB =4*\frac{13}{3}+15[/tex]
[tex]AB= \frac{52}{3}+15[/tex]
[tex]AB= \frac{97}{3}[/tex]
