Answer:
1. (a)4:1 (b)1:81 (c)9:25
2. (a)2:3 (b)4;5 (c)7:16
3. (a)3:5 (b)3:5 (c)9:25
Step-by-step explanation:
1. Given the ratio of similitude of two similar triangles, the ratio of their areas is the square of the ratio of similitude.
(a)2:1
Ratio of Area
[tex]=2^2:1^2\\=4:1[/tex]
(b)1:9
Ratio of Area
[tex]=1^2:9^2\\=1:81[/tex]
(c)3:5
Ratio of Area
[tex]=3^2:5^2\\=9:25[/tex]
2. Given the ratio of the areas of the sides of two similar polygons, the ratio of the sides is the ratio of the square root of their areas.
(a)4:9
Ratio of Sides [tex]=\sqrt{4} :\sqrt{9}=2:3[/tex]
(b)16:25
Ratio of Sides [tex]=\sqrt{16} :\sqrt{25}=4:5[/tex]
(c)49:256
Ratio of Sides [tex]=\sqrt{49} :\sqrt{256}=7:16[/tex]
3.Lengths of the Diameter are 6 and 10.
Diameter = Radius/2
Therefore, their radii are 3 and 5.
(a)Ratio of their Radii =3:5
(b)Since the circumference is still a length, Ratio of their Circumference =3:5
(c)Ratio of their Areas
[tex]=3^2:5^2\\=9:25[/tex]