Question

the length of a rectangle is three times its breadth.The perimeter of the rectangle is equal to that of a square whose area is 625cm^2.Find the area of the rectangle.​

Answer 1

Solution :

The area of the square is 625 cm² .

Let the side of the square be a .

Therefore , area of the square is a²

This implies that , a² = 625

a = | √625 | = 25 cm .

Perimeter of the square

=> 4 a

=> 4 × 25 cm

=> 100 cm .

Perimeter of square = Perimeter of rectangle

So , the perimeter of the rectangle is 100 cm .

The length is 3 times the breadth .

Suppose the breadth of the rectangle is x cm .

Length = 3x cm .

Perimeter = 2 [ Length + Breadth ]

=> 2 [ 4x ]

=> 8x = 100

=> x = 12.5 cm

3x = 37.5 cm

Area = Length × Breadth

=> 12.5 × 37.5

=> 468.75 cm²

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Answer 2

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$\huge{\boxed{\rm{\red{Question}}}}$

The length of a rectangle is three times its breadth.The perimeter of the rectangle is equal to that of a square whose area is 625cm^2.Find the area of the rectangle.

$\huge{\boxed{\rm{\red{Answer}}}}$

$\large\green{\texttt{The area of square is 625 cm²}}$

$\large\green{\texttt{Let side of square be x}}$

$\large\green{\texttt{Therefore area of square is a²}}$

$\large\green{\texttt{This tell that a² = 625 cm²}}$

$\large\green{\texttt{a = | √625 |}}$

$\large\green{\texttt{a = 25 cm}}$

$\large\green{\texttt{P of square = 4a}}$

$\large\green{\texttt{4 × 25 cm}}$

$\large\green{\texttt{100 cm}}$

Perimeter of square = Perimeter of rectangle.

$\large\green{\texttt{So the P of rectangle = 100 cm}}$

$\large\green{\texttt{L is 3 time than B}}$

$\large\green{\texttt{Let the L of rectangle = x}}$

$\large\green{\texttt{Length = 3x cm}}$

Perimeter of Rectangle = 2 ( Length + Breadth )

$\large\green{\texttt{2(4x) = 100}}$

$\large\green{\texttt{8x = 100}}$

$\large\green{\texttt{x = 12.5 cm}}$

$\large\green{\texttt{3x = 37.5 cm}}$

Area of Rectangle = Length × Breadth

$\large\green{\texttt{12.5 × 37.5}}$

$\large\green{\texttt{468.75 cm²}}$

@Itzbeautyqueen23

Hope it's helpful

Thank you :)