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
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
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