Solution:Concept- We will first let each side of the pentagon as and decagon be . Use the given condition to find the measure of each side of the decagon.
Let each side be of .
Hence, the perimeter of the pentagon is .
Then the sum of 10 sides is
Now, the measure of each side is
We know that the area of the pentagon is
Similarly, the area of the decagon is
Represent the ratio as a fraction.
We know that
On simplifying the above expression, we get
Then the above expression is simplified as,
Now, substitute the value of
Multiply numerator and denominator by to rationalise the denominator
Now, multiply numerator and denominator by
So, the ratio of the area of the pentagon to the area of the decagon is
Hence, the correct option is 2.