two similar figures have lengths in the ratio of 7/4. Give the ratios of parimeters and areas?
perimeter calculation is a linear measurement, so the perimeters are in the ratio of 7:4
but the area of two similar figures is in the ratio of the square of their sides, so
the areas are in the ratio of 49:16
To find the ratios of the perimeters and areas of two similar figures, we need to square the ratio of their lengths.
Given that the lengths of the two similar figures are in the ratio of 7/4, let's call this ratio k.
Ratio of perimeters:
The perimeter of a shape is the sum of the lengths of all its sides.
Since the lengths are in the ratio of k = 7/4, the ratio of perimeters will be k as well, which is 7/4.
Ratio of areas:
The area of a shape is a two-dimensional measurement and is proportional to the square of the lengths.
The square of the ratio k = (7/4)^2 = 49/16.
Therefore, the ratio of areas is 49/16.
So, the ratios of the perimeters and areas are:
Perimeters: 7/4
Areas: 49/16
To find the ratios of perimeters and areas of two similar figures, you need to understand the relationship between their corresponding side lengths.
Let's assume the lengths of the corresponding sides of the two similar figures are x and y respectively. According to the given information, the ratio of their lengths is 7/4, which means:
x/y = 7/4
To find the ratios of perimeters and areas, we need to consider the relationship between the corresponding sides.
1. Ratios of Perimeters:
The perimeter of a figure can be calculated by adding up all the side lengths. Since the two figures are similar, their corresponding sides are proportional. Therefore, the ratio of their perimeters will be the same as the ratio of their corresponding side lengths:
Perimeter ratio = (x + x + x + x + ...) / (y + y + y + y + ...)
Since the number of sides is the same for both figures, we can simplify the ratio and obtain:
Perimeter ratio = x/y
In this case, the perimeter ratio will be 7/4.
2. Ratios of Areas:
The area of a figure can be calculated by multiplying the base by the height. Since the two figures are similar, their corresponding sides are proportional. The ratio of their areas will be the square of the ratio of their corresponding side lengths:
Area ratio = (x * x * x * x * ...) / (y * y * y * y * ...)
Again, since the number of sides is the same for both figures, we can simplify the ratio and obtain:
Area ratio = (x/y)²
In this case, the area ratio will be (7/4)², which simplifies to 49/16.
Therefore, the ratios of perimeters and areas for the two similar figures are 7/4 and 49/16 respectively.