The numerical value of z in the expressions for the side lengths of the rectangle is 6.
The figure in the image is a rectangle.
It is simply quadrilateral having equal and parallel opposite sides.
The perimeter of a rectangle is expressed as:
Perimeter = 2( length + width )
From the figure:
Length = 4z + 3
Width = 3z + 1
Perimeter = 92 units
Plug the given values into the above formula and solve for z:
Perimeter = 2( length + width )
92 = 2( (4z + 3) + (3z + 1) )
92 = 2( 4z + 3 + 3z + 1 )
92 = 2( 7z + 3 + 1 )
92 = 2( 7z + 4 )
92 = 14z + 8
14z = 92 - 8
14z = 84
z = 84/14
z = 6
Therefore, the value of z is 6.