Question

if the breadth of a rectangle is increased by 3 cm and the length is reduced by 2 cm its area would increased by 20 sq cm but if the breadth is reduced by 2 cm and the length is increased by 1 cm the area would be reduced by 24 sq cm find the length and the breadth ​

Answer 1

★Answer:

Given:

• Breadth increased by 2 cm, length reduced by 2 cm, area increases by 20 cm²
• Breadth reduced by 2 cm, length increased by 1 cm, area reduced by 24 cm²

$\mathfrak{\underline{Solution:-}}$

Let the length be x , breadth be y

☘Formula to be used

$\boxed{\sf{Area \ of\ rectangle = length × breadth}}$

➣Putting the values ,

✮Area of rectangle = x × y = xy

✦Case I

When breadth is increased by 2 cm , length is reduced by 2 cm , area increases by 20 cm²

➣Forming the equation:

$\hookrightarrow$(x - 2)(y + 3) = xy + 20

$\hookrightarrow$xy + 3x - 2y - 6 = xy + 20

$\hookrightarrow$3x - 2y = 20 + 4

$\hookrightarrow$3x - 2y = 24⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-(1)

✦Case II

When breadth is reduced by 2 cm , length is increased by 1 cm, area is reduced by 24 cm²

➣Forming the equation:

$\hookrightarrow$(x + 1)(y - 2) = xy - 24

$\hookrightarrow$xy - 2x + y - 2 = xy - 24

$\hookrightarrow$-2x + y = -24 + 2

$\hookrightarrow$-2x + y = -22

$\hookrightarrow$-4x + 2y = -44⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀-(2)

✦Now adding the equations (1) , (2):

$\hookrightarrow$3x - 2y + (-4x + 2y) = 12 + (-44)

$\hookrightarrow$3x - 2y - 4x + 2y = 12 - 44

$\hookrightarrow$-x = - 32

$\hookrightarrow$x =32 cm

$\hookrightarrow$y = -22 + 2x = -22 + 2(32) = 64 - 22 = 42 cm

Hence , length and breadth are 32 cm and 42 cm respectively