#### Answer

A = 16x - $x^{2}$

#### Work Step by Step

The perimeter of rectangle is 32 cm where x is width and y is length
We need to express the area A of the rectangle in terms only of x
We know perimeter of rectangle is P = 2(L+B)
Given P =32 cm, l= y and b = x
32 = 2(y+x)
$\frac{32}{2}$ = y+x
16 = y+x
y = 16 - x cm ........ eq1
We know area of rectangle A = l*b
A = y *x
From eq1 put the value of y in area
A = (16 - x)*x
A = 16x - $x^{2}$