Question

The length of a rectangle is (x+1) cm, and its width is 5 cm less than its length.

a) Express the area of the rectangle, A cm^2 , in terms of x.
b) The area of the rectangle is 24 cm^2. Calculate the length and width of the rectangle.

Answer 1

a) x^2-3x-4(you also can express it as (x+1)(x-4))

b)The length is 8 cm, the width is 3 cm

Explanation:

a) The length is x+1

The width is (x+1-5)= x-4

The area is the product of the length and the width

(x+1)(x-4)= x^2-3x-4

b) The formula for counting the area is x^2-3x-4

It is equal to 24

S0 x^2-3x-4=24

x^2-3x-28=0

a=1 b=-3 c=-28

D= b^2-4ac= 3^2-4*(-28)= 9+112= 121

sqrtD= 11

x1= (-b-sqrtD)/2a=(3-11)/2=-4 The length is -4+1=-3<0, but the length must be positive, this root isn't suitable.

x2= (-b+sqrtD)/2a=(3+11)/2=7 The length is 7+1=8 (it is suitable)

8-5=3 - The width