The first thing to note is that the diagonals of any rhombus always bisect each other at a right angle
4x + 3 = 15
4x = 15-3
4x=12
x = 12/4
x = 3
To find y:
In the diagram above,
[tex]\begin{gathered} 17^{2\text{ }}=15^2+h^2 \\ 289=225+h^2 \\ h^2=\text{ 289-225} \\ h^2=64 \\ h=\sqrt[]{64} \\ h=8 \end{gathered}[/tex][tex]\begin{gathered} 2y\text{ - 4 = h} \\ 2y\text{ - 4 = 8} \\ 2y\text{ = 8+4} \\ 2y=12 \\ y=\frac{12}{2} \\ y=6 \end{gathered}[/tex]
To find the perimeter:
Perimeter of a rhombus = 4L ( where L is length of the one side)
Perimeter = 4 x 17 = 68
