Question

if perimeter of a Square and a rectangle are equal, which two has greater area?
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Answer 1

Answer:

If the perimeter of a square and a rectangle are equal, area of a square is greater than that of a rectangle.

Answer 2

Step-by-step explanation:

Given:-

perimeter of a Square and a rectangle are equal.

To find:-

which two has greater area?

Solution:-

If the side of a square "a" units then itsperimeter=4a units------(1)

If the length and breadth of a rectangle are "l" and "b"units then its perimeter=2(l+b) units----(2)

Given that

if perimeter of a Square and a rectangle are equal then

(1)=(2)

=>4a=2(l+b)

=>2a=l+b

=>a=(l+b)/2 units----(3)

Area of a square =a² sq. units

=>[(l+b)/2]²

=>(l+b)²/4 sq.units

=>a²= (l²+b²+2lb)/4

=>a²=(l²+b²)/4+(2lb/4)

=>a²=(l²+b²)/4+lb/2

a²=(l²+b²)/4+(area of a rectangle/2)

It is clear that

The area of a square is greater than the area of

a rectangle .

Answer:-

If the perimeters of a square and a rectangle are equal then the area of a square is greater than the area of the rectangle.