Mary has 62 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?
+1252 Q: Mary has 62 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?
A:
The more close in number the sides are, the greater the area.
For example, a square of side 5 has a greater area than a rectangle that is 3x7, even though both have the same perimeter.
Since there are four sides, and \(62\div 4\) equals 15.5, we know that the side lengths is somewhere around the range of 15 to 16.
However, We also need to account for the fact that the corners of the rectangle are overcounted, and since there are 4 corners, we need to add 4 to 62 and get 66.
Now, 66/4 = 16.5, and so the two side lengths are 16 and 17.
Now the part with the red tiles - if the side lengths are 16 by 17, then the area inside creates a 14 by 15 rectangle.
This is because each side has two tiles removed - the two sides.
Try drawing a 5x4 rectangle, and then see what the inside rectangle's dimensions is. It's a 3x2, or 5-2 x 4-2.
The last step is simply to multiply 14 by 15, which gets you 210.
Answer: 210 Red Tiles
You are very welcome!
:P
+1252 Q: Mary has 62 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?
A:
The more close in number the sides are, the greater the area.
For example, a square of side 5 has a greater area than a rectangle that is 3x7, even though both have the same perimeter.
Since there are four sides, and \(62\div 4\) equals 15.5, we know that the side lengths is somewhere around the range of 15 to 16.
However, We also need to account for the fact that the corners of the rectangle are overcounted, and since there are 4 corners, we need to add 4 to 62 and get 66.
Now, 66/4 = 16.5, and so the two side lengths are 16 and 17.
Now the part with the red tiles - if the side lengths are 16 by 17, then the area inside creates a 14 by 15 rectangle.
This is because each side has two tiles removed - the two sides.
Try drawing a 5x4 rectangle, and then see what the inside rectangle's dimensions is. It's a 3x2, or 5-2 x 4-2.
The last step is simply to multiply 14 by 15, which gets you 210.
Answer: 210 Red Tiles
You are very welcome!
:P
