Answer:
The width of the rectangular garden is 28 feet
Step-by-step explanation:
Let
x ----> the length of the rectangular garden in feet
y ---> the width of the rectangular garden in feet
we know that
The perimeter of the rectangular garden is equal to
[tex]P=2(x+y)[/tex]
we have
[tex]P=76\ ft[/tex]
so
[tex]76=2(x+y)[/tex]
simplify
[tex]38=x+y[/tex] ---> equation A
[tex]y=3x-2[/tex] ---> equation B
solve the system by substitution
substitute equation B in equation A
[tex]38=x+(3x-2)[/tex]
solve for x
[tex]38+2=x+3x[/tex]
[tex]4x=40\\x=10\ ft[/tex]
Find the value of y
[tex]y=3x-2[/tex] ---> [tex]y=3(10)-2=28\ ft[/tex]
therefore
The width of the rectangular garden is 28 feet
The width of rectangular garden is 28 ft.
Step-by-step explanation:
Given,
Fencing used to enclose the garden = 76 ft.
As it encloses the garden, it is the perimeter.
Let,
x be the length of rectangle.
Width = 3x-2
We know that;
Perimeter = 2(Length+Width)
[tex]76=2(x+3x-2)[/tex]
[tex]76=2(4x-2)\\76=8x-4\\76+4=8x\\80=8x\\8x=80[/tex]
Dividing both sides by 8
[tex]\frac{8x}{8}=\frac{80}{8}\\x=10[/tex]
Width = 3x-2 = 3(10)-2 = 30-2 = 28 ft.
The width of rectangular garden is 28 ft.
Keywords: perimeter, rectangle
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