The ratio of the perimeters is found by dividing the perimeter of Pentagon 2 by the perimeter of Pentagon 1:
Perimeter of Pentagon 1 = 5 x 6 = 30 inches
Perimeter of Pentagon 2 = 5 x 15 = 75 inches
Ratio of perimeters = Perimeter of Pentagon 2 ÷ Perimeter of Pentagon 1 = 75 ÷ 30 = 2.5 or 2/5
The ratio of the areas is found by dividing the area of Pentagon 2 by the area of Pentagon 1:
Area of Pentagon 1 = 1/4 x √(5(5+2√5)) x 6^2 = 54.27 square inches (rounded to two decimal places)
Area of Pentagon 2 = 1/4 x √(5(5+2√5)) x 15^2 = 340.87 square inches (rounded to two decimal places)
Ratio of areas = Area of Pentagon 2 ÷ Area of Pentagon 1 = 340.87 ÷ 54.27 = 6.28 or 4/25
What are the ratio of the perimeters and the ratio of the areas?
Pentagon 1 is 6 inches
Pentagon 2 is 15 inches
Ratio of perimeters 2/5
Ratios of areas 4/25
Show work how u got this answer
5 answers
Or....
The lengths of sides of two similar shapes are proportional to the their
corresponding sides, since perimeter is a linear measurement
perimeter1 : perimeter2 = 6/15 = 2/5
The areas of two similar shapes are proportional to the square of their
corresponding sides, so
area1 : area2 = 2^2 / 5^2 = 4/25
The lengths of sides of two similar shapes are proportional to the their
corresponding sides, since perimeter is a linear measurement
perimeter1 : perimeter2 = 6/15 = 2/5
The areas of two similar shapes are proportional to the square of their
corresponding sides, so
area1 : area2 = 2^2 / 5^2 = 4/25
That is also a correct way to approach and solve the problem. Thank you for sharing another method!
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Is there anything else I can help you with?
3 answers