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a) The distance around a rectangular room is 44 feet, and 120 tiles (each one is 1 sq. foot in size) are
needed to cover the floor of the room. What are the floor dimensions?

Answer :

Answer:

Step-by-step explanation:

let x and y be the sides of the rectangle.

2(x+y)=44

x+y=44/2=22

y=22-x

1 tile=1 sq. ft.

120 tiles=120 sq.ft.

area=120 sq.ft.

xy=120

x(22-x)=120

22x-x²=120

x²-22x+120=0

x²-12x-10x+120=0

x(x-12)-10(x-12)=0

(x-12)(x-10)=0

x=12,10

if x=12

y=22-12=10

if x=10

y=22-10=12

floor dimensions are 12 ft ×10 ft

The floor dimensions are 12 ft ×10 ft.

Let the length and breadth of the rectangle be x and y.

The perimeter of the rectangular room is P=2(x+y)

[tex]2(x+y)=44\\x+y=22\\y=22-x[/tex]

1 tile=1 sq. ft.

120 tiles=120 sq.ft.

Area of the rectangular room=120 sq.ft.

So, xy=120

Put y=22-x in xy=120

[tex]x(22-x)=120\\22x-x^{2} =120\\x^{2} -22x+120=0\\x^{2} -12x-10x+120=0\\x(x-12)-10(x-12)=0\\(x-12)(x-10)=0\\x=12,10[/tex]

if x=12then y=22-12=10

 if x=10 then y=22-10=12

 Therefore, the floor dimensions are 12 ft ×10 ft

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