Question

the perimeter of a rectangle is 240 cm if its length is decreased by 10%and its breath increased by 20%we get the same perimeter find the length and breadth of the rectangle

Answer 1

$\bold{firstly,}$

$\bold{\: Convert\: the\: new\: dimensions}$

to 9L and 1.2W

2L + 2W = 240

$\tt{simplify,\: divide\: by\: 2}$

L + W = 120

L = 120 - W, use for substitution

$\tt{new\: dimensions}$

2(.9L) + 2(1.2W) = 240

$\bold{simply}$$\bold{divide\: 2}$

9L + 1.2W = 120

$\bold{substitute}$, (120-W) in the above equation:

9(120-W) + 1.2W = 120

108 - .9W + 1.2W = 120
3W = 120 - 108

3W = 12

W = 12/.3

W = 40

$\bold{now,\: we\: have\: to\: find\: L}$

L = 120 - 40
L = 80

$\sf{solution,}$

2(80) + 2(40) = 240 and,

2(9*80) + 2(1.2*40) = 

144 + 96

= $\underline{240}$

Answer 2

Let the dimensions of the

rectangle are

i) length = x cm

breadth = y cm

Perimeter = 240 cm ( given )

2( x + y ) = 240

x + y = 120 ----( 1 )

If length is decreased by 10% and

breadth is increased by 20% then

the new dimensions are

Length = x ( 100-10)/100

= 90x /100

= 9x /10

Breadth = y× ( 100 +20 )/100

= 120y /100

= 12y /10

Perimeter = 240 cm

2 [ 9x /10 + 12y /10 ] = 240

9x + 12y = 1200

Divide each term with 3

3x + 4y = 400-----( 2 )

Multiply equation ( 1 ) with 3 and

Subtract from ( 2 )

y = 40

Put y = 40 in ( 1 )

x = 80

Therefore ,

Required rectangle dimensions are

Length = x = 80 cm

Breadth = y = 40 cm

I hope this helps u :)