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8. Aiden is replacing the tile in a rectangular kitchen. The length of the
kitchen is nine feet shorter than three times its width, w. The
perimeter of the kitchen is six times the width. If tiles cost $1.69 a
square foot, what is the total cost to tile the kitchen

How do you find the width

Answer 1

If the tiles cost $1.69 a square foot, the total cost to the tiles of the kitchen is $273.28.

According to the question:

Let the width be = x

Then, the length of the rectangular kitchen is L = 3x - 9

The perimeter is = 6x

It is given that the cost of the tile = $1.69 a square foot.

Then the total costs of tiles the kitchen is :

The Perimeter of the rectangle = 2(L + b)

The Perimeter of the rectangle = 2(3x - 9 + x)

The Perimeter of the rectangle = 2(4x-9)

We know that, according to the question,

the perimeter of the kitchen is six times the width = perimeter of rectangle

⇒ 6x = 8x - 18

⇒ - 2x = - 18

⇒ x = 18/2

⇒ x = 9

Thus, the width = x = 9 feet

Putting the value of x = 9

then, The length = 3x - 9 = 3(9) - 9

the length = 27 - 9

the length = 18 feet

Therefore, as we know that,

Area = Length × Width

Area = (18 × 9) feet

Area = 162 square feet.

Now,

Cost of a Tile = $1.69 per sq. ft.

Thus,

Total Cost of tile = $1.69 × 162

Total Cost of tile = $273.28