Respuesta :
Answer:
A) A = W(W + 4)
B) Length = 7 ft
Width = 3 ft
Step-by-step explanation:
A) Let the length and width of the rectangular rug be L and W respectively.
We are told that the rug is 4 feet longer than it is wide. Thus;
L = (W + 4)
Also we are told that the area is 21 ft²
Now, formula for area of a rectangle is;
A = LW.
Thus;
A = W(W + 4)
21 = W(W + 4)
B) 21 = W² + 4W
W² + 4W - 21 = 0
Using quadratic formula to find the roots, we arrive at W = 3 ft.
Thus, L = 3 + 4 = 7 ft
The equation to determine the length and width of the rug is
[tex]w^2+4w-21=0[/tex]
Length of rug = 7 feet
width of the rug = 4 feet
Rectangle:
A rectangle is a four sided figure with opposite sides are equal .
Area of rectangle.
Area of a rectangle = Length * width
Given : A rectangular rug with an area of 21 square feet.
The rug is 4 feet longer than it is wide.
Let 'l be the length of the rug and 'w' be the width of the rug
Length 'l' is 4 feet longer than its width
[tex]l = w+4\\[/tex]
Area is 21 square feet.
Area = length * width
[tex]A= l \cdot w\\21=(w+4)w\\21=w^2+4w\\w^2+4w-21=0\\(w+7)(w-3)=0\\w+7=0, w=-7\\w-3=0, w=3[/tex]
The equation to determine the length and width of the rug is
[tex]w^2+4w-21=0[/tex]
width cannot be negative . So width = 3 ft
Length = w +4
length = 3+4= 7 feet
Length of the rug is 7 feet
Length of rug = 7 feet
width of the rug = 4 feet
Learn more information about ' Area of rectangle ' here
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