A rectangular rug has an area of 60 in.². What are the dimensions, in inches, if the perimeter of the rug is 34 in.?
O A. 3, 20
O B. 5, 12
O C. -5, -12
O D. -3, 20
What are the dimensions of a rectangular rug with an area of 60 in.² and a perimeter of 34 in.?
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To solve this problem, we need to find the dimensions (length and width) of the rectangular rug that has an area of 60 in² and a perimeter of 34 in.
1. Area of the rug:
[
text{Area} = text{length} times text{width} = 60 quad (1)
]
2. Perimeter of the rug:
[
text{Perimeter} = 2 times (text{length} + text{width}) = 34 quad (2)
]
Dividing this equation by 2 gives:
[
text{length} + text{width} = 17 quad (3)
]
3. Now, we can set up a system of equations using (1) and (3):
[
text{width} = 17 – text{length} quad (4)
]
Substituting equation (4) into equation (1):
[
text{length} times (17 – text{length}) = 60
]
This expands to:
[
17text{length} – text{length}^2 = 60
]
Rearranging gives:
[
text{length}^2 – 17