The ratio of their area is 81 : 1.
Step-by-step explanation:
Given,
The perimeter of two equilateral triangles is 9:1
To find the ratio of their areas.
Formula
If each side of a equilateral triangle is a then perimeter = 3a and area = [tex]\frac{\sqrt{3} }{4}[/tex]a²
Now,
Perimeter of the 1st triangle is 9x
So, each side will be 3x
Again,
Perimeter of the 2nd triangle is x
So, each side will be [tex]\frac{x}{3}[/tex]
Now,
Area of the 1st triangle =[tex]\frac{\sqrt{3} }{4}[/tex](3x)²
Area of the 2nd triangle = [tex]\frac{\sqrt{3} }{4}[/tex]([tex]\frac{x}{3}[/tex])²
Hence,
The ratio of their area = [tex]\frac{\sqrt{3} }{4}[/tex](3x)² :
= 9x² : [tex]\frac{x^{2} }{9}[/tex]
= 81 : 1
Thus the obtained ration of the triangle is 81:1
