Question

the perimeter of a rectangle is 240 CM. If its length is increased by 10% and its breadth is decreased by 20% we get the same perimeter. find the length and breadth of the rectangle.

Answer 1

let lenght be x and breath be y
length = x ; breadth = y
perimeter = 2(x +y ) = 240
                 = x + y = 120                - (i)
new length = 10/100 * x + x
                    = x/10 + x
                    = 11x/10
new breadth = y - 20/100*y
                      = y - y/5
                      = 4y/5
perimeter= 2 ( 11x/10 + 4y/5)
                = 2 ([11x + 8y]/10)
                = 11x + 8y / 5 = 240
                11x + 8y = 1200
so x = [1200 - 8y] / 11
put this value in 1st equation,
[1200-8y] / 11 +y = 120
[1200 - 8y+11y] /11 = 120
1200 +3y = 1320
3y = 1320-1200
3y=120
y=40
put this value in 1st equation
x + y = 120
x + 40 = 120
x = 80
so, x = 80; y = 40
 

Answer 2

$\huge{\underline{\underline{\sf{\red{SOLUTION:-}}}}}$

$\sf{\underline{\blue{Answer-}}}$

• Length of the rectangle = 80cm.

• Breadth = 40 cm.

$\sf{\underline{\blue{Given-}}}$

• Perimeter of a rectangle is 240 CM. If its length is increased by 10% and its breadth is decreased by 20% we get the same perimeter.

$\sf{\underline{\blue{We\:Have\:Find-}}}$

• Length and breadth of the rectangle.

$\sf{\underline{\blue{Explanation-}}}$

$\sf {Perimeter \: of \: rectangle \: = 240cm}$

$\sf{2(length \: + \: breadth) \: = \: 240 \: cm}$

$\sf{ \: Length \: + \: breadth \: = \frac{240}{2} = 120cm}$

$\sf{Let \: the \: Length \: be \: x \: cm.}$

$\sf{Then \: , \: breadth \: = \: (120-x)cm}$

$\sf{Length\: is \: increased\: by \:10\%}$

$\sf{ New \: length = x + \frac{10}{100} x = \frac{11x}{10} m}$

$\sf{Breadth \: is \: decreased \: by \: 20\%}$

$\sf New\:Breadth=(120+x)- \frac{20}{100} \times (120 - x)$

$\sf (120-x) [1- \frac{1}{5}] = (120 - x) \times \frac{4}{5}cm$

⠀

$\bf{Given}: Perimeter \: remains \: same.$

⠀

➨⠀$\sf\: 2[ \frac{11x}{10} + (120 - x) \times \frac{4}{5} ] = 240$

➨⠀$\sf \frac{11x}{10} + \frac{480\:-\:4x}{5} = 120$

➨⠀$\sf \frac{11x\:+\:960\:+\:8x}{10} = 120$

➨⠀$\sf 3x \: + \: 960=120×10$

➨⠀$\sf 3x \: + \: 960=1200$

➨⠀$\sf 3x=1200-960$

➨⠀$3x = 240$

➨⠀$\sf x= \frac{240}{3} = 80.$

⠀

$\bf{Hence,}$

⠀

• $\sf{length \: of \: the \: rectangle=80cm}$

• $\sf{Breadth = 120 - 80=40cm.}$