A 30 foot by 24 foot carpet has a white center whose area is 432 square feet. The carpet also has a dark grey border and the top, bottom, and side parts of this border have the same width,
a.
Write an equation using the variable that would allow you to find the width of the border.
b.
Solve your equation to find the width of the border. Show your work. Include proper units in your
answer. Write your final answer in the shaded box.

a) (30 - 2x) * (24 - 2x) = 432

b) 3 inches

Step-by-step explanation:

Let's call the width of the border 'x'.

So the length of the white center is 30 - 2x, and the width is 24 - 2x.

Then, we have that the white center area is:

(30 - 2x) * (24 - 2x) = 432

720 - 108x + 4x2 = 432

4x2 - 108x + 288 = 0

x2 - 27x + 72 = 0

Using Bhaskara's formula to solve the quadratic equation, we have:

Delta = 27^2 - 288 = 441

sqrt(Delta) = 21

x1 = (27 + 21)/2 = 24 (Not a reasonable answer, as the length and width of the center area would be negative)

x2 = (27 - 21)/2 = 3

So the dark grey border has a width of 3 inches

answer:

total cost for tiles and paints is $924.  

step-by-step explanation:

we have been given that a community hall is in the shape of a cuboid. the hall is 40m long 15m high and 3m wide.

the paint will be required for 4 walls and ceiling.

let us find area of walls and ceiling.

therefore, the area of walls and ceiling is 1410 square meters.

given: cost for 10 litre of paint is $10 and 10 litre paint covers 25 square meter. therefore,

therefore, the total painting cost is $564.

tiles will be required for floor. let us find the area of floor.

given: 1m squared floor tiles costs $3. so,

therefore, the total tiles cost is $360.

now let us find combined total cost of tiles and paint.

therefore, the combined total cost of tiles and paint is $924.