Mathematics
Grade9
Easy

Question

The two figures are similar. Find the ratios (red to blue) of the perimeters and of the areas.

  1. Perimeter = 11: 6, Area = 121:36
  2. Perimeter = 6:11, Area = 36:121
  3. Perimeter = 36:121, Area = 6:11
  4. Perimeter = 121:36, Area = 11:6

hintHint:

ratio of perimeter = ratio of sides
Ratio of area = (ratio of perimeter)2

The correct answer is: Perimeter = 11: 6, Area = 121:36


    perimeter = 11:6 and area = 121: 36

    We know that ratio of perimeter = ratio of sides
    Given, ratio of sides = 11: 6
    Ratio of area = (ratio of perimeter)2
    Ratio of area = (11/6)^2 = 121:36

    Perimeters: The scale factor and the perimeters' ratios are identical. The scale factor is the same for any ratio between two similar shapes (diagonals, medians, midsegments, altitudes, etc.).
    Area: The area is the region defined by an object's shape. The area of an object shape is the space covered by a figure or any two-dimensional geometric shape in a plane. All shapes' areas are determined by their dimensions and properties. Different shapes have various areas.Area of Rectangle = a × b

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