Question

a living room rug is 9 ft by 12 ft a strip of floor of equal width is uncovered on all sides of the room if the area od the uncovered floor is 270 ft^2 how wide is the strip

Answer 1

Explanation:

To find the width of the strip of uncovered floor, we need to subtract the area of the covered floor from the total area of the room, and then divide by the width of the strip.

The total area of the room is:

9 ft x 12 ft = 108 ft^2

Let's assume the width of the strip is x.

Then the dimensions of the covered floor are:

Length = 9 - 2x Width = 12 - 2x

The area of the covered floor is:

(9 - 2x) x (12 - 2x) = 108 - 30x + 4x^2

We know that the area of the uncovered floor is 270 ft^2, so we can set up the equation:

108 - 30x + 4x^2 = 270

Simplifying and rearranging:

4x^2 - 30x - 162 = 0

Dividing by 2:

2x^2 - 15x - 81 = 0

Using the quadratic formula:

x = [15 ± sqrt(15^2 + 4(2)(81))]/4

x = [15 ± sqrt(1089)]/4

x = [15 ± 33]/4

x = 12 or x = -3/2

Since the width of the strip cannot be negative, we can discard the negative root, and the width of the strip is:

x = 12/2 = 6 ft

Therefore, the strip of uncovered floor is 6 ft wide.