Question

The area of a rectangular park is same as the area of a square park. If the side of the square park is 60 m and the length of the rectangular park is 80 m, find the breadth of the rectangular park​

Answer 1

$\underline{ \underline{ \Large \pmb{\sf { \purple{Answer:}} }} }$

• Breadth of the rectangular park is 45 m.

$\underline{ \underline{ \Large \pmb{\sf { \purple{Given:}} }} }$

• Area of rectangular park = Area of square park

• Side of the square park = 60m

• Length of the rectangular park = 80 m

$\underline{ \underline{ \Large \pmb{\sf { \purple{To \: calculate:}} }} }$

• Breadth of the rectangular park.

$\underline{ \underline{ \Large \pmb{\sf { \purple{Calculation:}} }} }$

As per the given question, the area of the rectangular park and area of the square park is same and we have been given its square park's side and rectangular park's length. We have to find the breadth of the rectangular park. We'll form an algebraic equation and by solving that equation we'll find the measure of breadth.

⠀⠀⠀⠀⠀_____________

According to the question,

$\longrightarrow \sf \purple { {Area}_{(Square \: park)} = {Area}_{(Rectangle \: park)} }$

We know that,

• Area of square = Side × Side
• Area of rectangle = Length × Breadth

$\longrightarrow \sf {Side \times Side = Length \times Breadth }$

As,

• Side of the square park = 60 m [Given]
• Length of the square park = 80 m [Given]

$\longrightarrow \sf {60 \: m \times 60 \: m = 80 \: m \times Breadth }$

$\longrightarrow \sf {3600 \: m^2 = 80 \: m \times Breadth }$

$\longrightarrow \sf {\dfrac{3600 \: m^2}{80 \: m} = Breadth }$

$\longrightarrow \boxed{ \pmb {\sf\purple {45 \: m= Breadth} }}$

Therefore,

• Breadth of the rectangular park is 45 m.

$\underline{ \underline{ \Large \pmb{\sf { \purple{Verification:}} }} }$

As per the provided question,

$\longrightarrow \sf \red { {Area}_{(Square \: park)} = {Area}_{(Rectangular \: park)} }$

LHS :

→ Area of the square park

→ Side × Side

→ 60 m × 60 m

→ 3600 sq. m

RHS:

→ Area of the rectangular park

→ Length × Breadth

→ 80 m × 45 m

→ 3600 sq. m

• LHS = RHS

Hence, verified!

Answer 2

ar(rectangular park) = ar(square park)

We know,

• Area of a rectangle = l × b
• Area of square = s²

As per condition,

lb = s²

⇒ 80b = 60 × 60

⇒ 8b = 6 × 60

⇒ b = 45 m.

Therefore, the breadth of the Rectangular Park is of 45 m.