Answer:
Perimeter of larger triangle is 40.
Step-by-step explanation:
Given:
Perimeter of smaller circle = 16
Ratio of corresponding side = 2:5
We need to find the perimeter of the larger triangle.
Solution:
Let the perimeter of the larger triangle be 'x'.
Therefore by theorem which states that;
" When a triangle have scale factor a:b then the ratio of the perimeters is a:b".
Here Ratio is 2:5, so we can say by theorem, Ratio of perimeters is 2:5
framing in equation form we get;
![\frac{\textrm{Perimeter of smaller triangle}}{\textrm{Perimeter of Larger triangle}}=\frac{2}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ctextrm%7BPerimeter%20of%20smaller%20triangle%7D%7D%7B%5Ctextrm%7BPerimeter%20of%20Larger%20triangle%7D%7D%3D%5Cfrac%7B2%7D%7B5%7D)
Substituting the values we get;
![\frac{16}{x}=\frac{2}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7Bx%7D%3D%5Cfrac%7B2%7D%7B5%7D)
By Cross multiplication we get;
![16\times 5=2x\\\\80=2x](https://tex.z-dn.net/?f=16%5Ctimes%205%3D2x%5C%5C%5C%5C80%3D2x)
Dividing both side by 2 we get;
![\frac{80}{2}=\frac{2x}{2}\\\\x=40](https://tex.z-dn.net/?f=%5Cfrac%7B80%7D%7B2%7D%3D%5Cfrac%7B2x%7D%7B2%7D%5C%5C%5C%5Cx%3D40)
Hence Perimeter of larger triangle is 40.