Question

If a square and a rectangle are equal in area, then:
a) Their perimeters are always same
b) Perimeter of square is larger than the perimeter of the rectangle.
c) Perimeter of rectangle may be larger than the perimeter of the square.
d) Nothing can be observed about their perimeters.​

Answer 1

Answer:

perimeter of square is larger than perimeter of rectangle

Answer 2

Perimeter of rectangle may be larger than the perimeter of the square if a square and a rectangle are equal in area

Given :  A square and a rectangle are equal in area

To Find : Choose Correct Statement

a) Their perimeters are always same

b) Perimeter of square is larger than the perimeter of the rectangle.

c) Perimeter of rectangle may be larger than the perimeter of the square.

d) Nothing can be observed about their perimeters.​

Solution:

Square perimeter  =  4 * side

Square  Area  = side²

Rectangle Perimeter  = 2( length + width )

Rectangle Area = length * width

For a given area of a rectangle , square has the least perimeter.

Proof

rectangle length = l   width = w

Area A = lw

Perimeter  = 2(l + w)

P(w) = 2(A/w  + w)

P'(w) = 2(-A/w² + 1)

P'(w) = 0

=> w²  = A

P''(w) = 2(2A/w³) > 0 Hence minimum perimeter

When A = w²

=> lw = w² => l = w

Hence a square

A square and a rectangle are equal in area Hence Perimeter of rectangle may be larger than the perimeter of the square.

Correct option is c)

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