Question

What are a) the ratio of the perimeters and b) the ratio of the areas of the larger figure to the

smaller figure? The figures are not drawn to scale

Answer 1

keeping in mind that the ratio of the sides is the same as the ratio of the perimeters, Check the picture below.

Answer 2

The ratio of perimeters is 5:2 and the ratio of the areas is 15:2.

Ratios for the two figures:

a) Ratio of perimeters:

Perimeter of larger figure (30 yards side) = 4 * 30 yards = 120 yards

Perimeter of smaller figure (12 yards side) = 4 * 12 yards = 48 yards

Ratio of perimeters = Perimeter of larger figure / Perimeter of smaller figure = 120 yards / 48 yards = 5:2

b) Ratio of areas:

Area of larger figure (30 yards side) = 30 yards * 30 yards = 900 square yards

Area of smaller figure (12 yards side) = 12 yards * 12 yards = 144 square yards

Ratio of areas = Area of larger figure / Area of smaller figure = 900 square yards / 144 square yards = 15:2