Question

A rhombus is inscribed in a rectangle that is w meters wide with a perimeter of 24 m. Each vertex of the rhombus is a midpoint of a side of the rectangle. Express the area of the rhombus as a function of the​ rectangle's width.

Answer 1

P=2(L+W)
P=24
24=2(L+W)
12=L+W
L=12-W
area of the rhombus
see diagram
as you can see, the area of the rhombus is 1/2LW
L=12-W
area=(1/2)(12-W)(W)
$A(W)= \frac{12W-W^2}{2}$