Question

the area of a rectangle is sum as that of a square of side 60 M if the length of the rectangle is 32 metre find its perimeter​

Answer 1

GIVEN :

Side of square = 60m

Length of rectangle = 32

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1st we have to find Are of square

$\green{ \large \boxed{ \bf Area \: of \: Square = {a}^{2} }}$

$\bf Area = 60 \times 60 \\ \\ \bf Area = 3600 {m}^{2}$

Area of Square = Area of Rectangle

$l \times b = 3600 {m}^{2} \\ \\ 32 \times b = 3600 \\ \\ b = \frac{3600}{32} \\ \\ \large \boxed{ \red{ \bf b = 112.5}}$

Now we can find Perimeter of Rectangle

$\bf Perimete \: of \: Rectangle = 2(l + b) \\ \\ \Longrightarrow2(32 + 112.5) \\ \\ \Longrightarrow2 \times 144.5 \\ \\ \Longrightarrow 289$

$\large \boxed{ \blue{ \bf Perimeter = 289m}}$

Answer 2

Correct Question :

• The area of a rectangle is same as that of a square of side 60m, if the length of the rectangle is 32m then, find the perimeter of the Rectangle.

Given :-

• The area of a rectangle = The Area of a Square
• Side of Square = 60m
• Length of the Rectangle = 32m

To Find :-

• The perimeter of Rectangle

Solution :-

❏ For finding the Perimeter of the Rectangle, we need Length and Breadth of the Rectangle and Length is given. It is also given that The area of a rectangle = The Area of a Square . Therefore :

➞ Area of Square = Area of Rectangle

➞ (Side)² = Length × Breadth

➞ Side × Side = Length × Breadth

➞ 60 × 60 = 32 × Breadth

➞ 3600 = 32 × Breadth

➞ 3600 / 32 = Breadth

➞ 112.5m = Breadth

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⟼ Perimeter of Rectangle = 2 ( L + B )

⟼ Perimeter of Rectangle = 2 ( 32 + 112.5 )

⟼ Perimeter of Rectangle = 2 × 144.5

⟼ Perimeter of Rectangle = 289m

Thus, Perimeter of Rectangle is 289m

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★ Additional Info :

Formulas Related to Rectangle :

• Perimeter of Rectangle = 2( l + b)
• Area = Length × Breadth
• Length = Area / Breadth
• Breadth = Area / Length
• Diagonal = √(l)² + (b)²

Formulas Related to Square :

• Perimeter = 4 × Side
• Area = Side × Side
• Side of Square = √Area
• Diagonal = √2 × Side
• Area = ½ × (Diagonal)²
• Area = (Perimeter ÷ 4)²

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