Quadratic Functions.............................

Question

Application of quadratic equation and quadratic functions

 

(1) The Length of a rectangular rug is twice its width .If the area of the rug is 450 square feet, Find the length and width of the rug.

 

(2) The Length of a rectangular room is 1 foot more than twice its width.If the area of the room is 300 square feet,Find the length and width of the room.

 

 

 

Answer 1

Let w=width of rug

2w=length of rug

w×2w=2w²=area=450

w²=225

w=15 and so 2w=30

 

w=width

length=2w+1

area=w(2w+1)=2w²+w=300

2w²+w-300=0

(2w+25)(w-12)=0

w=12 is only positive root

length=25

Answer 2

1) Let the width of the rectangular rug is x

         The Length of the rectangular rug will be 2x

Area is L*W= x*2x=450sq ft

2x^2= 450 sq ft

x^2=450/2=225

x=15ft

Width is 15 Ft

Length is 2*15=30 ft

 

 

2)

Let the width of the room is Y ft

Length of the room will be 2Y+1 ft

Area = Length*Width=Y*(2Y+1)= 300 sq ft

2Y^2+Y=300

2Y^2+Y-300=0

Take out the factor for 600 (2*300)

2Y^2-24Y+25Y-300=0

2Y(Y-12)+25(Y-12)=0

(2Y+25)(Y-12)=0

Y=-25/2 , 12

measurement can't be negative, so Y=12 ft

Width of the room=12 ft

Length of the room= 12*2+1=24+1=25

check L*W=12*25=300