Question

If the areas of two similar decagons are 625 ft^2 and 100 ft^2, what is the ratio of the perimeters of the decagons? tf is a decagon ????

Answer 1

`\text{Answer: }\frac{\text{ Perimeter of first decagon}}{\text{ Perimeter of second decagon}}=(5)/(2)`

Explanation:

Since we have given that

Area of two similar decagons are 625 ft² and 100 ft² ,

As we know the relation of area of similar figures, i.e.

`\frac{\text{ Area of first decagon}}{\text{ area of second decagon}}=(625)/(100)=(a^2)/(b^2)`

Now, we also know that ,

`\frac{\text{ Perimeter of first decagon}}{\text{ Perimeter of second decagon}}=(a)/(b)=(√(625))/(√(100))=(25)/(10)=(5)/(2)`

Hence,

`\frac{\text{ Perimeter of first decagon}}{\text{ Perimeter of second decagon}}=(5)/(2)`