Question

Cynthia Besch wants to buy a rug for a room that is 29 ft wide and 30 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 756 square feet of carpeting. What dimension should the rug have?

Answer 1

Dimensions of rug:

Length = 28 ft

Width = 27 ft

Explanation:

The given dimensions of the room is:

Length = 30 ft

Width = 29 ft

Area of carpeting = 756 sq ft

Kindly refer to the attached image.

Let the uniform strip around floor is of length =
`x` ft

This
`x` feet will be 2 times along the length and

2 times along the width of room.

So, length of rug = 30 -2
`*`
`x` and

Width of rug = 29 -2
`*`
`x`

It will be rectangular in shape.

Area of a rectangle is given as:

`A = Length* Width`

`756 = (30-2x) (29-2x)\\\Rightarrow 756 = 870 - 118x+4x^2\\\Rightarrow 4x^2-118x+114=0\\\Rightarrow 2x^2-59x+57=0\\\Rightarrow 2x^2-57x-2x+57=0\\\Rightarrow x =1, -(57)/(2)`

Negative length not possible.

So,Length of strip,
`x = 1\ ft`

Dimensions of rug:

Length = 30 -2 = 28 ft

Width = 29 -2 = 27 ft