Two corresponding sides of similar polygons are in the ratio of 5:4. If the perimeter of the smaller figure is 40, what is the perimeter of the larger figure?
The ratio is 5:4. Therefore, anything with a measure of 4 in the smaller has a measure of 5 in the larger.
So what would something with a measure of 40 in the smaller have in the larger?
To find the perimeter of the larger figure, we need to determine the ratio between the perimeters of the two polygons. Since two corresponding sides of similar polygons are in the ratio of 5:4, it means that the ratio of their perimeters will also be 5:4.
Let's represent the perimeter of the smaller figure as "P". According to the given information, P = 40.
To find the perimeter of the larger figure, we can set up a proportion using the ratio of the perimeters:
(P perimeter of smaller figure) / (P perimeter of larger figure) = 5/4
Substituting the value we know, we have:
40 / (perimeter of larger figure) = 5/4
To solve for the perimeter of the larger figure, we can cross-multiply:
4 * 40 = 5 * (perimeter of larger figure)
160 = 5 * (perimeter of larger figure)
Next, we isolate the perimeter of the larger figure by dividing both sides of the equation by 5:
160 / 5 = perimeter of larger figure
32 = perimeter of larger figure
Therefore, the perimeter of the larger figure is 32.