Respuesta :
Answer:
The width of the yard will be = 200 ft
The length of the yard will be = 900 ft
Step-by-step explanation:
Given:
Ratio of width to length of a rectangular yard = 2 : 9
The distance around the yard = 2200 ft
To find the dimensions of the yard.
Solution:
Let the width of the rectangular yard be = [tex]2x[/tex]
So, the length of the yard will be = [tex]9x[/tex]
The perimeter of a rectangle is given as:
[tex]P=2(l+w)[/tex]
where [tex]l[/tex] represents length and [tex]w[/tex] represents width of the rectangle.
Plugging in the given values of length and width of the yard.
[tex]P=2(9x+2x)[/tex]
Simplifying.
[tex]P=2(11x)[/tex]
[tex]P=22x[/tex]
The perimeter given = 2200 ft.
Thus, the equation to find [tex]x[/tex] can be given as:
[tex]22x=2200[/tex]
Dividing both sides by 22.
[tex]\frac{22x}{22}=\frac{2200}{22}[/tex]
∴ [tex]x=100[/tex]
The width of the yard will be = [tex]2\times 100 = 200\ ft[/tex]
The length of the yard will be = [tex]9\times 100 = 900\ ft[/tex]
