Question

If the perimeter of a rectangle is equal to the perimeter of a square with sides 4m each and the length of the rectangle is thrice its breadth, then the area of the rectangle would be??​

Answer 1

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Answer 2

Answer:

The area of the Rectangle is 12 m².

Step-by-step explanation:

Given :

Perimeter of the rectangle = Perimeter of the Square

Side of the Square = 4 m

To find :

Area of the rectangle

Solution :

$\textsf{\underline{\underline{Perimeter of the square - }}}$

★ Perimeter = 4 × Side

$\sf{\implies} \: 4 \times 4 \\ \\ \sf{\implies} \: 16$

Perimeter = 16 m

$\rule{300}{1.5}$

$\textsf{\underline{\underline{Dimensions of the rectangle - }}}$

Let the -

• Breadth be y
• Length be 3y

★ Perimeter = 2(Length + Breadth)

$\sf{\implies} \: 16 = 2(3y + y) \\ \\ \sf{\implies} \: 16 = 6y + 2y \\ \\ \sf{\implies} \: 16 = 8y \\ \\ \sf{\implies} \: y = \dfrac{16}{8} \\ \\ \sf{\implies} \: y = 2$

Breadth = 2 m

$\rule{300}{1.5}$

★ Value of 3y

$\sf{\implies} \: 3(y) \\ \\ \sf{\implies} \: 3(2) \\ \\ \sf{\implies} \: 6$

Length = 6 m

$\rule{300}{1.5}$

$\textsf{\underline{\underline{Area of the rectangle -}}}$

★ Area = Length × Breadth

$\sf{\implies} \: 6 \times 2 \\ \\ \sf{\implies} \: 12$

Area = 12 m²

$\therefore$ The area of the Rectangle is 12 m².