Mr. Dieter wants to tile the family room in his basement. He has selected a pattern of square tiles that measure 9 inches by 9 inches each. The shape of the floor to be tiled is shown below. a. What is the area of the family room in square feet? b. How many of the 9 inch by 9 inch tiles will it take to cover the floor? (NOTE: You will need to convert the area in Part a from square feet to square inches.) c. If the tile is sold only in boxes of 12 tiles per box, how many boxes will Mr. Dieter have to buy to tile the family room?

146 ft²

21.6 tiles

1.8 boxes

Step-by-step explanation:

Please find attached an image of the family room used in answering this question

the family room has the following shapes : 2 triangles and one rectangle

the area of the family room can be determined by calculating the area of each of the shape and adding the 3 areas together

area of a rectangle = length x breadth

16 x 7 = 112 ft²

Area of a triangle = 1/2 x base x height

Area of the smaller triangle = (1/2) x 4 x 3 = 6 ft²

Area of the bigger triangle = (1/2) x 8 x 7 = 28 ft²

Sum of the areas = 112 + 6 + 28 = 146 ft²

b.

1. First convert the area of the room to inches

1 ft = 12 in

146 x 12 = 1752 in²

2. the next step is to determine the area of the tile

area of a square = length²

9² = 81 in²

3. Divide the area of the room by the area of the tile

1752 / 81 = 21.6 tiles

c. total number of boxes that would be bought = 21.6 /12 = 1.8 boxes

80% of the cookies

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240