What are the dimensions of a rectangular rug with an area of 60 in.² and a perimeter of 34 in.?

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