Math, asked by nmsujay11, 14 hours ago

The perimeter and area of a rectangular play ground are 80m and 384m2 respectively. Find the length and breadth of the play ground.द सम ऑफ टू नेचुरल नंबर्स इज 9 एंड द सम ऑफ द रिसिप्रोकल इज 9 डिवाइडेड बाय टू फाइंड द नंबर ​

Answers

Answered by Anonymous
0

Step-by-step explanation:

Solution

let say Length = x m

Breadth Bm =

2(length + breadth ) = Perimeter

Expressing It

=> 2(x + B) = 80

=> x + B = 40

=> B = 40 -x m

Area = Length * Breadth

=> 384 = x ( 40 - x)

=> 384 = 40x - x²

=> x² - 40x + 384 = 0

=> x² -24x - 16x + 384 = 0

=> (x-24)(x - 16) = 0

=> x = 24 or 16

=> 40 -x = 16 or 24

length and breadth are 16 & 24 m

Answered by jatinsahu718
0

Step-by-step explanation:

Given

Perimeter of rectangle= 80m²

Area of Rectangle= 384m²

To Find

Length and Breadth

Formula used

\boxed{\underline{Perimeter~of~Rectangle=2(Length+Breadth)}}

Perimeter of Rectangle=2(Length+Breadth)

\begin{gathered}\boxed{\underline{Area \: of \: Rectangle=Length×Breadth}}\\\end{gathered}

AreaofRectangle=Length×Breadth

Let

Length be l

Breadth be b

\begin{gathered}\\\sf~~~ Perimeter~of~Rectangle= 2(Length+Breadth)\end{gathered}

Perimeter of Rectangle=2(Length+Breadth)

{→\sf 2(Length+Breadth)=80}→2(Length+Breadth)=80

{→\sf\cancel{2}(Length+Breadth)=\cancel=80}→

2

(Length+Breadth)=

=

80

{→\sf Length+Breadth=40}→Length+Breadth=40

\begin{gathered}{→\sf Breadth=40-Length}\\\\\end{gathered}

→Breadth=40−Length

\begin{gathered}\boxed{\underline{Area \: of \: Rectangle=Length×Breadth}}\\\end{gathered}

AreaofRectangle=Length×Breadth

Putting the Value of Breadth in Formula We get

\begin{gathered}\\{→\sf384=Length×(40-Length)}\end{gathered}

→384=Length×(40−Length)

{→\sf (Length)^{2} - 40Length+ 384 =0 }→(Length)

2

−40Length+384=0

{→ \sf(Length)^{2} - 24Length - 16Length+ 384 =0 }→(Length)

2

−24Length−16Length+384=0

{→\sf Length(Length - 24)- 16(Length+ 24) =0 }→Length(Length−24)−16(Length+24)=0

\begin{gathered}{→\sf ( Length - 16 ) (Length - 24)=0 }\\\\\end{gathered}

→(Length−16)(Length−24)=0

Length of playground= 24 cm

Breadth of playground =16 cm

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