Question

The length of a square shaped garden is 40 m. The length and breadth of another rectangular garden are respectively 50 m and 30 m. Find the perimeter of both gardens. Which garden has more area and by how much? Show answer with proper steps and diagram.​

Answer 1

Answer :-

Given :-

• Length of square garden is 40 m.

• Length and breadth of rectangular garden are 50 m and 30 m respectively.

To Find :-

• Perimeter of both gardens.
• Which garden has more area.

Solution :-

Square :-

$\begin{gathered}\begin{gathered} \sf40 \: m \: \: \: \: \: \: \: \: \: \: \: \\ {\boxed{\begin{array}{}\bf { \red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}} { \sf\:40 \: m} \end{gathered}\end{gathered}$

Perimeter of square = 4 × Side

= 4 × 40

= 160

Perimeter of square = 160 m

Area of square garden = Side × Side

= 40 × 40

= 1600

Area of square garden = 1600 m²

Rectangle :-

$\begin{gathered}\begin{gathered} \sf 50\:m \: \: \: \: \: \: \: \: \: \: \: \\ \boxed{\begin{array}{}\bf { \red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}} \sf\:30\:m \end{gathered}\end{gathered}$

Perimeter of rectangle = 2 ( Length + Breadth )

= 2 ( 50 + 30 )

= 160

Perimeter of rectangle = 160 m

Area = Length × Breadth

= 50 × 30

= 1500

Area of rectangular garden = 1500 m²

Area of square garden > Area of rectangular garden

Area of square garden - Area of rectangular garden = 1600 - 1500

= 100

Square garden is 100 m more than that of rectangular garden.

Answer 2

Answer :

• Area of the square garden is 100 sq.m more then the area of the rectangular garden.

Given :

• Length of square garden = 40 m
• Length and breadth of rectangular garden = 50 m and 30 m

To Find :

• the perimeter of both gardens.
• Which garden has more area ?

We know :

• Square = side × side
• Rectangle = length × breadth

_____________________

Square garden :

Diagram :

$\huge \boxed{\begin{gathered}{ \: \: \: \: \: \: \: \: } \end{gathered}} \\ \bf{40 \: m}$

Solution :

Length of square garden = 40 m

Perimeter = 4 × length of the side ( a )

• = 4 × a
• = 4 × 40 m
• = 160 m

Area = ( side )²

• = ( 40 m )²
• = 1600 sq.m

_____________________

Rectangular garden :

Diagram :

$\huge\boxed{ \begin{gathered}{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \end{gathered}} \small{ \bf{ \: 30 \: m}} \\ \bf{50 \: m} \: \: \: \: \: \: \: \: \:$

Solution :

Length of rectangular garden = 50 m

Breadth of rectangular garden = 30 m

Area = Length × Breadth

• = 50 m × 30 m
• = 1500 sq.m

Perimeter = 2 × ( l + b )

• = 2 × ( 50 + 30 ) m
• = 2 × 80 m
• = 160 m

_____________________

Therefore, The area of the square garden is ( 1600 - 1500 ) = 100 sq.m more than the area of the rectangular garden.