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?
1 Answer
48 inches
Explanation:
The two rectangles are similar, meaning the ratios between length and width are the same.
We know the length of the red tile (6 inches), but we don't know the width. We do know, since the two rectangles are similar, 10 is to 30 as 6 is to the width of the red tile. 30 is 3 times larger than 10, so the width of the red tile must be 3 times larger than the length of the red tile, meaning it must be 3 times larger than 6.
That produces 18 as the width of the red tile.
Since the perimeter is just the sum of all the side lengths, then we can just add up all the side lengths. One of the defining features of the rectangle is 2 sets of congruent (same size) sides. Therefore, there are two sides with length 6, and two sides with length 18.
Then we add up those sides. 18+18+6+6=48
So the perimeter must be 48 inches.
