Question

The figures to the right are similar. Compare the first figure to the second. Give the ratio of the perimetersand the ratio of the areas.The ratio of the perimeters is(Type an integer or a simplified fraction.)The ratio of the areas is(Type an integer or a simplified fraction.)

Answer 1

Given data:

Side of first figure (a1) = 12 cm

Side of second figure (a2) = 30 cm

Now, The perimeter of first figure,

P1 = 4 a1

= 4 x 12

= 48

The perimeter of second figure,

P2 = 4 a2

= 4 x 30

= 120

Ratio of the perimeters,

`\begin{gathered} (P1)/(P2)=(48)/(120) \\ \text{ = }(2)/(5) \end{gathered}`

Now, The area of first figure

A1 = a1 x a1

= 12 x 12

= 144

The area of second figure,

A2 = a2 x a2

= 30 x 30

= 900

The ratio of the areas,

`\begin{gathered} (A1)/(A2)=(144)/(900) \\ \text{ = }(6)/(25) \end{gathered}`