Question

the length of a rectangular playground is thrice its breadth. if the perimeter of the playground is 56 meters, find its dimension.
​ᴡʜᴀᴛ ɪꜱ ᴛʜᴇ ᴀɴꜱᴡᴇʀ​

Answer 1

Answer:

Breadth= 7 m

Length= 21 m.

Step-by-step explanation:

Question-

the length of a rectangular playground is thrice its breadth. if the perimeter of the playground is 56 meters, find its dimension.

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Given-

Perimeter of the playground.

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To Find-

Dimensions (length and breadth) of the playground.

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Solution-

Let's take the breadth as 'x'.

Then, length = 3x.

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With the given perimeter, we will find the dimensions of the playground.

Formula = $\color{black}\boxed{\colorbox{saffron}{Perimeter-2(length+breadth) }}$

$56 = 2(x + 3x) \\ \\ 56 = 2(4x) \\ \\ 56 = 8x \\ \\ \frac{56}{8} = x \\ \\ 7 = x$

So, x=7.

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Required Answer-

$\rightarrow$ Breadth = x = 7m

$\rightarrow$ Length = 3x = 3×x = 3×7= 21 m.

Answer 2

DIAGRAM :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 3x m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large x m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

$\: \:$

$\bold{Given}\begin{cases} \sf \: Length \: of \: a \: rectangular \: playground \: is \: thrice \: its \: breadth. \\ \\ \sf \: Perimeter \: of \: the \: playground \: is \: \bold{56 \: m}.\end{cases}$

$\: \:$

Need to find : Dimensions of the rectangular playground.

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀____________________

Let the breadth of the rectangular playground be x

$\: \:$

So,

$\:$

• Length of the rectangular playground will be 3x

$\: \:$

Here perimeter of the rectangular playground is given as 56m.

$\: \:$

For finding the perimeter of a rectangle, formula is given as :

$\:$

$\star\underline{\boxed{\sf\pink{Perimeter_{(rectangle)} = 2(l + b)}}} \:$

$\:$

Where, l denotes length of the rectangle and b denotes breadth of the rectangle.

$\:$

$\sf:\implies \: Perimeter_{(rectangle)} = 2(l + b) \\ \\ \\ \sf:\implies \: Perimeter_{(rectangle)} =2(x + 3x) \\ \\ \\ \sf:\implies \: 56 = 2(x + 3x) \\ \\ \\ \sf:\implies \cancel \frac{56}{2} = 4x \\ \\ \\ \sf:\implies \: 4x = 28 \\ \\ \\ \sf:\implies \: x = \frac{28}{4} \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{x = 7}}} \: \bigstar$

$\: \:$

Now,

$\: \:$

• Breadth of the rectangular playground = x = 7m
• Length of the rectangular playground = 3x = 3(7) = 21m

$\: \:$

$\sf \therefore{ \underline{Hence, \: the \: dimensions \: of \: the \: rectngular \: playground \: is \: \bold{7m} \: and \: \bold{21m} \: respectively.}}$