a blue rectangular tile and a red rectangular tile are similar. the blue tile has a length of 10 inches and a perimeter of 30 inches. the red tile has a length of 6 inches. what is the perimeter of the red tile?
18
P = (6/10) * 30 = 18 Inches.
To find the perimeter of the red tile, you need to use the information given about the blue tile. Since the blue and red tiles are similar, we can use the ratio of their lengths to find the ratio of their perimeters.
Let's set up a proportion to find the ratio of the perimeters:
Blue length : Red length = Blue perimeter : Red perimeter
Given:
Blue length = 10 inches
Blue perimeter = 30 inches
Red length = 6 inches
Using the formula for the perimeter of a rectangle (Perimeter = 2 * (length + width)), we have:
Blue perimeter = 2 * (10 + width)
Red perimeter = 2 * (6 + width)
Now, we can set up the proportion:
10 : 6 = 30 : x
Cross-multiplying, we get:
10x = 6 * 30
Simplifying, we have:
10x = 180
Dividing both sides of the equation by 10, we find:
x = 18
Therefore, the perimeter of the red tile is 18 inches.