The widths of two similar rectangles are 10 m and 8 m. What is the ratio of the perimeters? Of the areas?
(1 point)
A.6:5 and 36:25
B. 5:4 and 36:25
C. 5:4 and 25:16
D.6:5 and 25:16
To find the ratio of the perimeters, we can compare the lengths of the two rectangles. Since the rectangles are similar, we can use proportions to find the length of the larger rectangle.
Let x be the length of the smaller rectangle.
The ratio of the widths is 10:8, which can be simplified to 5:4.
Setting up a proportion, we have:
10/5 = x/4
Cross-multiplying, we get:
10 * 4 = 5x
40 = 5x
x = 8
Therefore, the length of the larger rectangle is 8.
The perimeter of the smaller rectangle is 2(10 + 8) = 36 units.
The perimeter of the larger rectangle is 2(8 + 8) = 32 units.
The ratio of the perimeters is 36:32, which simplifies to 9:8.
To find the ratio of the areas, we can use the formula for the area of a rectangle: length * width.
The area of the smaller rectangle is 10 * 8 = 80 square units.
The area of the larger rectangle is 8 * 8 = 64 square units.
The ratio of the areas is 80:64, which simplifies to 20:16 or 5:4.
Therefore, the correct answer is option C. 5:4 and 25:16.