# Math

posted by .

a rectangle of integer dimensions is filed with 1x1 tiles. Each tile that touches the perimeter is colored red, while all the "interior" tiles are left white. Let R be the number of red tiles and W the number of whites tiles

find R and W for a 3x10 rectangle

find any and all rectangles for which R and W are equal

Find any and all rectanglef for which R is twice the size of W

Find any and all rectanlges for which E is twice the size of R

• Math -

for the 3x10
total squares = 30
inner W's = 1x8 = 8
Reds = 30-8 = 12

In general
let width be x, and length be y
total squares = xy
W = (x-2)(y-2) = xy -2x -2y + 4
then R = xy - (xy - 2x - 2y +4)
= 2x + 2y - 4

for R = W
2x+2y-4 = xy - 2x - 2y + 4
4x+4y-8=xy
4y - xy = 8-4x
y(4-x) = 8-4x
y = (8-4x)/(4-x) = 4(x-2)/(x-4)
so pick any value of x , x>4 , and y an integer.
e.g. x = 8, then y = 6
x=12, y= 5
x = 60 , y ≠ integer
since the function approaches 4 as x gets larger, and we are already at y = 5 when x=12
the only two cases are :
8 by 6 or 12 by 5

for R = 2W , try it yourself
for the last one, I don't know what E is . Did you mean W ?

## Similar Questions

1. ### math

TILING A decroative floor pattern has one red square tile surrounded by 12 blue tiles. Write and evaluate an expression to show how many total tiles (red and blue) are needed if there are 15 red tiles. Then make a table showing the …
2. ### !!MATH!!

A decroative floor pattern has one red square tile surrounded by 12 blue tiles. Write and evaluate an expression to show how many total tiles (red and blue) are needed if there are 15 red tiles. Then make a table showing the total …
3. ### Math

Ben has 8 square tiles. Each tile has a width of 9 inches. He lays the tiles down in a long row. What is the perimeter of the rectangle of tiles?
4. ### Algebra

Marco is making mosaic garden stones using red, yellow, and blue tiles. He has 45 red tiles, 90 blue tiles, and 75 yellow tiles. Each stone must have the same number of each color tile. What is the greatest number of stones Marco can …
5. ### Algebra

A class of 23 students was using square tiles to build rectangular shapes. Each student had more than 1 tile and each had a different number of tiles. Each student was able to build only one shape of rectangle. All tiles had to be …
6. ### Math accelerated

A decorative floor pattern has 1red square tile surrounded by 12 blue tiles.write and evaluate an expression to show how many total red and blue tiles are needed if there are 15 red tiles. Then make a table showing the total number …
7. ### Computer

Suppose there are b black, w white and r red tiles on a table. We are allowed to replace two tiles of different colors with the third color. Note one thing here that this third colored tile is from our pool containing infinite black, …
8. ### Math

A class of 23 students was using square tiles to build rectangular shapes. Each student had more than 1 tile and each had a different number of tiles. Each student was able to build only one shape of rectangle. All tiles had to be …
9. ### Maths

Mary has 6262 square blue tiles and a number of square red tiles. All tiles are the same size. She makes a rectangle with red tiles inside and blue tiles on the perimeter. What is the largest number of red tiles she could have used?
10. ### mathematics

A bag contains 6 red tiles, 8 blue tiles, and 6 green tiles. A tile is drawn, the color recorded, and then the tile placed back in the bag before a tile is drawn again. if this procedure is done 30 times, how many red tiles would you …

More Similar Questions