Question

The shortest sides of two similar polygons have lengths in the ratio 2:5. The perimeter of the smaller polygon is 20. The perimeter of the larger polygon is

Answer 1

A similar triangle has the same ratio on every side, so that means the perimeter has the same ratio as well.
Set up the proportion: 2/5 = 20/x
multiply the means and extremes to get
2x = 100
divide both sides by 2
x = 50
The perimeter of the larger polygon is 50
Hope this helped =)

Answer 2

The perimeter of the larger polygon is 20 units.

Explanation:

We know that,

The ratio of the perimeters of two similar polygons is equal to the ratio of the corresponding sides of the polygons.

Here, the ratio of the corresponding sides of smaller and larger polygon is 2 : 5,

Also, given,

Perimeter of shorter polygon is 20 units,

Let x be the perimeter of the larger polygon,

By the above property,

`\implies (2)/(5)=(20)/(x)`

`\implies 2x = 100` ( By cross multiplication )

`\implies x = 50`

Hence, the perimeter of the larger polygon is 20 units.