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

Answer:

Dimensions of rug:

Length = 28 ft

Width =  27 ft

Step-by-step 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 $\times$ $x$ and

Width of rug = 29 -2 $\times$ $x$

It will be rectangular in shape.

Area of a rectangle is given as:

$A = Length\times Width$

$756 = (30-2x) (29-2x)\\\Rightarrow 756 = 870 - 118x+4x^2\\\Rightarrow 4x^2-118x+114=0\\\Rightarrow 2x^2-59x+57=0\\\Rightarrow 2x^2-57x-2x+57=0\\\Rightarrow x =1, -\dfrac{57}{2}$

Negative length not possible.

So,Length of strip,  $x = 1\ ft$

Dimensions of rug:

Length = 30 -2 = 28 ft

Width = 29 -2 = 27 ft