Question

a rectangle and a sqare are equal in area the side of the squares is 24 m if the length of the rectangle is 36 m find the breadth of the rectangle comment on their perimeters ​

Answer 1

Answer:

breadth of the rectangle is

[4 × 24 - (36 × 2)] ÷ 2

= [4 × 24 - 72] ÷ 2

= (96 - 72) ÷ 2

= 24 ÷ 2

= 12m

The perimeter of both the rectangle and square will be same

square = 24 × 4

= 96m

rectangle = 2 × (l + b)

= 2 × (12 + 36)

= 2 × 48

= 96m

Answer 2

$\boxed{\huge{\bf{AnswEr-:}}}$

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$\sf{Breadth\:of\:Rectangle\: -:16m}$

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$\large{\sf{\star{Formulas\:related\:to\:question}}}$

• Area of Rectangle-:

“A = l x b”

• Area of Square-:

“A = s x s”

• Perimeter of Rectangle-:

“P = 2(l + b)”

• Perimeter of Square-:

“P = 4 x S”

Here,

P = Perimeter

L = length of rectangle

B = breadth of rectangle

S = length of side of a square

A = Area

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$\large{\sf{\star{Given\:-:}}}$

• Area of Square is equal to tha area of

Rectangle

• Length of side of a square-:24 m

• Length of the Rectangle-: 36 m

$\large{\sf{\star{To\:Find\:-:}}}$

• The breadth of Rectangle.

• The perimeter of rectangle and square.

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$\large{\sf{\star{Solution\:-:}}}$

$\sf{\star{Area \: of \: Square-:}}$

$\sf{A = s \times s}$

$\sf{S \:= length \:of \:side \:of \:a \:square -: \: 24m}\\\\{\sf{A =\: Area \:=?? }}$

Now ,

$\sf{\rightarrow{24 \times 24}}$

$\sf{\rightarrow{576cm^{2}}}$

Now ,

$\sf{\rightarrow{Area\:of\:square\:576m^{2}}}$

$\sf{Given \:that}\\\\{\sf{Area\:of\:Rectangle\:is\:equal\:to\:the\:area\:of\:square}}$

$\sf{Area\:of\:Rectangles\:-:\:576m^{2}}$

Then,

$\sf{Area\:of\:Rectangle\: -:}\\\\{\sf{A = l \times \: b}}$

$\sf{l\: = length \:of\:Rectangle\:-:36m}\\\\{\sf{b\:=\:breadth\:of\: Rectangle =\:??}}\\\\{\sf{Area\:of\:Rectangles\:-:\:576m^{2}}}$

Now,

$\sf{\rightarrow{36\times b= 576}}$

$\sf{\rightarrow{b =\frac{576}{36}}}$

$\sf{\rightarrow{b =16}}$

Therefore,

$\sf{Breadth\:of\:Rectangle\: -:16m}$

•Perimeter of Rectangle-:

“P = 2(l + b)”

• Length of breadth of a Rectangle -:16m

• Length of the Rectangle-: 36 m

$\sf{\rightarrow{2\times (36\:+16)}}$

$\sf{\rightarrow{2\times 52}}$

Therefore,

• Perimeter of Rectangle-: 104 m

Then,

• Perimeter of Square-:

“P = 4 x S”

S = length of side of square = 24

Now,

$\sf{\rightarrow{4\times 24}}$

$\sf{\rightarrow{96m}}$

Therefore,

•Perimeter of Square-: 96m

$\large{\sf{\star{Hence\:-:}}}$

$\sf{Breadth\:of\:Rectangle\: -:16m}$

Now ,

• Perimeter of Rectangle-: 104 m

•Perimeter of Square-: 96m

$\sf{Here\:, \:We \:see \:that\: the}\\\\{\sf{perimeter\:of\:Rectangle\:is\:greater \:than }}\\\\{\sf{the\:perimeter\:of\:square.}}$

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