Question

The ratio of the areas of two similar polygons is 121:225. If the perimeter of the first polygon is 60 cm, what is the perimeter of the second polygon?

Round to the nearest tenth please!

Answer 1

The perimeter of the second polygon is 81.82 cm.

Explanation:

Since area for a polygon can be expressed as
`Area = sidex^(2)`, then we can express the ratios in the same form:

`(121)/(225) =(11^(2) )/(15^(2) )`

We obtained from here that the ratio of the side is 11:15. Now, remember that perimeter is
`Perimeter=4*side`, then the ratio of perimeters will be also 11:15. To find the area of the second polygon, we establish a ratio equation:

`(11)/(15) =(60)/(A_(2) )`

Applying cross multiplication:

`11*A_(2)=15*60\\A_(2)=(15*60)/(11) \\A_(2)=81.82 cm`