1.

If the perimeter of a square and rectangle is 100.Find whose area is more by how much?​

Answer»

\Large{\underline{\underline{\mathfrak{\bf{<klux>QUESTION</klux>}}}}}

If the PERIMETER of a square and RECTANGLE is 100.Find whose area is more by how much ?

\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}

\Large{\underline{\mathfrak{\bf{\pink{Given}}}}}

  • perimeter of a square = 100 units
  • Perimeter of a rectangle = 100 units
  • perimeter of a square = Perimeter of a rectangle

\Large{\underline{\mathfrak{\bf{\pink{Find}}}}}

  • Find whose area is more by how much?

\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}

Let,

Length and breadth of a rectangle is x and y .

So,

★ Perimeter of rectangle = 2( x + y )

★ perimeter of square = (side)²

A/c to question ,

( perimeter of a square = Perimeter of a rectangle )

➥ 4(side) = 2( x + y )

➥ Side of square = 2.(x+y)/4

➥ Side of square = (x+y)/2 units

★ Area of square = (side)²

So,

➥ Area of square(S) = (x+y)²/4 units² ....(1)

★ Area of rectangle(R) = x.y units² .......(2)

Subtract equ(2) - equ(1)

➥ R - S = (x.y) - (x+y)²/4

➥ R - S = { 4x.y - (x²+y²+2.xy)}/4

➥ R - S = { -x² - y² + 2.xy}/4

➥ R - S = - ( x² + y² - 2.xy)/4

➥ R - S = -(x - y)²/4

Therefore, R - S = Negative quantity.

Thus,

  • S > R

Hence,

Area of square greater than area of rectangle ( Answer)

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