Math, asked by vasant7, 1 year ago

the area of a rectangular carpet is 120 m 2 and its perimeter is 40 cm the length of the diagonals is

Answers

Answered by abhi569
2


let the length of rectangle be x and breadth be y

then 

area of rectangle = length * breadth

here,  area of rectangle= l*b = lb

120 =l*b 

120 = lb                   --------------------1equation

Now,

perimeter of rectangle = 2(l+b)

here,  40 = 2(l+b) 

40/2= l+b

20 = l+b           -----------------2equation

as by pythagoras theorem,

diagonal^2= l^2 +b^2

Now,

by formula (a+b)^2  = a^2 +b^2 +2ab

(l+b)^2 = l^2  + b^2 +2lb

putting the values from equation 1&2,

(20)^2 = l^2 + b^2 +(2*120)

400  = l^2 + b^2 +240

400-240 = l^2 + b^2

160 = l^2 +b^2                -----------------3equation

then 

diagonal^2= l^2  + b^2

putting the value of l^2 +b^2  from 3equation

diagonal^2 = 160

then 

diagonal  = root 160

diagonal = 12.63  cm 

i hope this will help you 

-by ABHAY

abhi569: if cost of fencing is 25
abhi569: then perimeter of square = 2000/25
abhi569: perimeter = 80
abhi569: perimeter of square = 4*side
abhi569: niow
abhi569: now,
abhi569: 4*x= 80
abhi569: x= 40/4
abhi569: x= 20
abhi569: the side of feild is 20m
Answered by Cutiepie93
5
Hlo friend.. Cutiepie Here...

Here is ur answer :

Area of a rectangular carpet = 120 m²

Let length be l and breadth be b.

Length × breadth = 120

lb = 120 ____________ (1)


Perimeter of Rectangular carpet = 40 cm

2 ( length + breadth) = 40

2 ( l + b) = 40

( l + b) = 40 / 2

( l + b) = 20 ___________(2)


Diagonal D of Rectangular carpet =
 \sqrt{ {(length)}^{2} +  {(breadth)}^{2}  }


 \sqrt{ {l}^{2}  +  {b}^{2} }


By using identity,

( a + b)² = a² + b² + 2ab

Putting the values from eqⁿ (1) and (2)

( l + b)² = l² + b² + 2lb

(20)² = l² + b² + 2(120)

400 = l² + b² + 240

l² + b² = 400 - 240

l² + b² = 160


Diagonal =
 \sqrt{ { l}^{2} +  {b}^{2}  }


 \sqrt{160}


 = 12.64



Diagonal D of Rectangular carpet = 12.64 cm.


________________

HOPE IT HELPS YOU..
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