SOLUTION: Three shapes- a circle, a rectangle, and a square- have the same area. Which shape has the smallest perimeter?

Question 556429: Three shapes- a circle, a rectangle, and a square- have the same area. Which shape has the smallest perimeter?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Circle -- a bit tricky to prove using elementary geometry techniques, but we can definitely find an example. For example, suppose that the area of each shape is 1. It can easily be shown that the rectangle with fixed area and the minimal perimeter is a square. The perimeter of the square is 4, and now you can just find the radius of the circle with area 1, then find the circumference.
RELATED QUESTIONS
shape P is a rectangle of length 4cm and breadth 6cm and shape Q is a square both shapes... (answered by josgarithmetic)

A square, an equilateral triangle and a circle all have the same perimeter. Which one has (answered by math_tutor2020,ikleyn)

Among the following shapes of equal perimeter, which one has the largest area ?... (answered by edjones)

A square and a circle have equal areas. Which shape has shorter... (answered by Fombitz)

A square and a circle have equal areas. Which shape has shorter... (answered by Jk22)

An octagon, a triangle and a circle all have the same distance around That's perimeter... (answered by Edwin McCravy)

A farmer has 114 feet of fencing. Which shape would give the most area? (a) Equilateral... (answered by math_tutor2020)

a. Draw 4 different rectangles, all of which have an area of 4 square inches. Label your... (answered by Edwin McCravy)

A rectangle has area of 600 square meters. its length and width are whole number which... (answered by Alan3354,solver91311)