Question

The area of a square and rectangle are equal.If the side of a square is 28 m and the length of rectangle is 49 m ,find the breadth of the rectangle. Also find the perimeter of the rectangle.​

Answer 1

Answer:

The area of square=The area of rectangle

area of square=side×side

=28×28

=784

As we know area of square is equal to area of rectangle

therefore,the area of rectangle is 784

length of rectangle=49

breadth=x

784=49×x

x=784/49

x=16

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Answer 2

Step-by-step explanation:

Given:-

• The area of a square and rectangle are equal.

• The length of the rectangle = 49m

• The side of the square = 28m

To Find:-

• The breadth of the rectangle.

• The perimeter of the rectangle.

Solution:-

Side of the square = 28m

$\sf Area \: of \: the\: square = (Side)^{2}$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 28^{2}$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 784m^2$

Length of the rectangle = 49m

Let the breadth of the rectangle = x

$\sf Area \: of \: the\: rectangle = Length \times Breadth$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 49x$

$\sf Area\: of \: the\: rectangle = Area \: of \: the\: square$

$\sf \implies 49x = 784$

$\sf \implies x = \dfrac{784}{49}$

$\sf \implies x = 16$

$\sf \therefore \underline{\: \: \underline{\: Breadth \: of \: the \: rectangle = 16m \:}\: \:}$

$\sf Perimeter \: of\: the \: rectangle = 2(Length + Breadth)$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 2(49 + 16)$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:= 2 \times 65$

$\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 130m$

$\underline{\boxed{\therefore \textsf{\textbf{Perimeter \: of \: rectangle = 130m}}}}$