Two corresponding sides of similar polygons have the ratio 5:4. The perimeter of the smaller figure is 40, what is the perimeter of the larger figure...I need help trying to figure this out...and the steps!
To solve this problem, let's go step by step:
Step 1: Determine the scale factor
The scale factor is the ratio between corresponding sides of two similar figures. In this case, the ratio is 5:4 for the corresponding sides. To find the scale factor, divide the larger side length by the smaller side length. So, in this case, the scale factor is 5/4.
Step 2: Find the length of each side of the larger figure
Since the scale factor is 5/4, you can multiply each side length of the smaller figure by the scale factor to find the corresponding side length of the larger figure. The perimeter of the smaller figure is given as 40, so each side length of the smaller figure is 40/4 = 10. Therefore, each side length of the larger figure is 10 * (5/4) = 12.5.
Step 3: Calculate the perimeter of the larger figure
Since the larger figure has four sides, we can multiply the length of each side (12.5) by 4 to find the perimeter. Therefore, the perimeter of the larger figure is 12.5 * 4 = 50.
So, the perimeter of the larger figure is 50.
To find the perimeter of the larger figure, you need to determine the ratio of their perimeters using the given ratio of their corresponding sides. Here's how you can solve the problem step by step:
Step 1: Understand the problem
Similar polygons have corresponding angles that are congruent, and corresponding sides that are in proportion. In this case, the ratio of the corresponding sides is given as 5:4.
Step 2: Find the scale factor
The scale factor is the ratio of the corresponding sides. In this case, the scale factor is 5:4.
Step 3: Find the perimeter of the smaller figure
The perimeter of the smaller figure is given as 40.
Step 4: Determine the scale factor of perimeters
Since the scale factor for the sides is 5:4, the scale factor for the perimeters will also be 5:4. This means that the perimeter of the larger figure is 5/4 times the perimeter of the smaller figure.
Step 5: Calculate the perimeter of the larger figure
To find the perimeter of the larger figure, multiply the perimeter of the smaller figure by the scale factor for perimeters:
Perimeter of the larger figure = (Perimeter of the smaller figure) * (Scale factor for perimeters)
= 40 * (5/4)
= 50
Therefore, the perimeter of the larger figure is 50.
In summary:
- First, find the scale factor for the sides, which is 5:4.
- Then, find the perimeter of the smaller figure, which is 40.
- Next, determine the scale factor for the perimeters, which is also 5:4.
- Finally, calculate the perimeter of the larger figure by multiplying the perimeter of the smaller figure by the scale factor for perimeters, which gives you a perimeter of 50 for the larger figure.
"Similar" is a vague term. If the polygons are congruent (the same shape), then
5:4::x:40 or
5/4 = x/40
Solve for x.