# Chapter 8 - Section 8.1 - Area and Initial Postulates - Exercises - Page 361: 52

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 - $x^{2}$

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