If a square of side 8 m and a rectangle of length 12 m have the same perimeter, then find the area of the rectangle (in $m^{2}$ ).

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Solution

The perimeter of a square = 4 × side

Perimeter of a rectangle = 2 (length + breadth)

Given, the perimeter of the square = perimeter of the rectangle

⇒ 4 × 8 = 2(12 + b)

⇒ 32 = 24 + 2b

⇒ 2b = 32 - 24

⇒ 2b = 8

⇒ b = 4 m

$∴$ Area of the rectangle = l × b = 12 × 4 = 48 $m^{2}$

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If a square of side 8 m and a rectangle of length 12 m have the same perimeter, then find the area of the rectangle (in m2).

The perimeter of a square = 4 × side Perimeter of a rectangle = 2 (length + breadth) Given, the perimeter of the square = perimeter of the rectangle ⇒ 4 × 8 = 2(12 + b) ⇒ 32 = 24 + 2b ⇒ 2b = 32 - 24 ⇒ 2b = 8 ⇒ b = 4 m ∴ Area of the rectangle = l × b = 12 × 4 = 48 m2

If a square of side 8 m and a rectangle of length 12 m have the same perimeter, then find the area of the rectangle (in $m^{2}$ ).

The perimeter of a square = 4 × side

Perimeter of a rectangle = 2 (length + breadth)

Given, the perimeter of the square = perimeter of the rectangle

⇒ 4 × 8 = 2(12 + b)

⇒ 32 = 24 + 2b

⇒ 2b = 32 - 24

⇒ 2b = 8

⇒ b = 4 m

$∴$ Area of the rectangle = l × b = 12 × 4 = 48 $m^{2}$