Question

a rectangle and a square are equal in area. the side of the square is 24 metre. if the length of the rectangle is 36 metre, find the breadth of the rectangle . comment on their parameters

answer - 16m, perimeter of rectangle = 104m, perimeter of square =96m.​

Answer 1

Given

Rectangle and square are equal in area i.e.

$lb = a^{2}$ ... eqn (i)

where l and b are length and breadth of rectangle

and a is side of square

Also

a = 24 m

and l = 36 m

Using these values in eqn (i)

36 b = 24*24

36b = 576

b = 576/36

b = 16

Thus Breadth is of 16 m

Now

Parameter of square = 4a = 4(24) = 96 m

And

Parameter of rectangle = 2(l+b) = 2(36+16)

= 2(52) = 104 m

Thus

parameter of square is 96m

and parameter of rectangle is 104m

Parameter of rectangle is more than square by 8 metres.

Answer 2

Step-by-step explanation:

Given that,

• A rectangle and a square are equal in area.
• Each side of the square is 24 metres and the length of the rectangle is 36metres.

Here,

→ Area of the square = Area of the rectangle.

Step 1 :

Area of the rectangle is given by : l • b

• l (length) = 36m (given)
• b (breadth) = ?

So, Area of the rectangle = 36 • b

Step 2 :

Area of a square : ( each side )²

• Each side = 24m (given)

So, area of the square = ( 24 )²

→ 576m²

Step 3 :

→ Area of the square = Area of the rectangle (given)

→ 576 = 36 • b

→ 576/36 = b

→ b = 16m

∴ Therefore, the breadth of the rectangle is 16metres.

_____________________

Finding their perimeters :

Perimeter of rectangle is given by :

→ 2( l + b )

From the given dimensions :

→ 2(36 + 16)

→ 2(52)

→ 104metres.

Perimeter of a square : 4 • side

• each side is 24 metres (given)

→ 4 • 24

→ 96metres.

∴The perimeter of rectangle is 104 and square is 96metres.