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

$\text{Answer: }\frac{\text{ Perimeter of first decagon}}{\text{ Perimeter of second decagon}}=\frac{5}{2}$

Step-by-step 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.

$\frac{\text{ Area of first decagon}}{\text{ area of second decagon}}=\frac{625}{100}=\frac{a^2}{b^2}$

Now, we also know that ,

$\frac{\text{ Perimeter of first decagon}}{\text{ Perimeter of second decagon}}=\frac{a}{b}=\frac{\sqrt{625}}{\sqrt{100}}=\frac{25}{10}=\frac{5}{2}$

Hence,

$\frac{\text{ Perimeter of first decagon}}{\text{ Perimeter of second decagon}}=\frac{5}{2}$