2 The perimeter of rectangle is 20 meters if we varies the l

2) The perimeter of rectangle is 20 meters, if we varies the lengths of two sides, by assuming the length of one side x (a) write down a function expressing the area of the rectangle. (b) What are the domain and the range of the function? (c) What is maximum area? (d) When the area of the rectangle is 18 square meters, find the length of the two sides of the rectangle

Solution

perimeter = 20 metres

length of one side = x

let width = y

2( x+y) = 20

x + y = 10

y = 10 - x

area of rectangle = length * width

A(x) = x ( 10- x)

A(x) = -x^2 + 10x

b) domian is all values of x that the function can take in

domain of this function is [ 0 , 10 ]

range is all y values for which the function exists

range is [ 0 , 25 ]

c) maximum area occurs at

x = - 10 / 2(-1) =5

maximum area = -(5)^2 +10(5) = 25

d) when area = 18 square metres

x(10-x) = 18

10x - x^2 = 18

x^2 - 10x + 18 = 0

x = 7.645

y = 2.355

so, length = 7.645

width = 2.355