Question

The length of a rectangle is 4 cm more than its breadth.If the length is inceased by 4 cm and breadth
decreased by 2 cm. the area remains the same as of that original rectangle.Find the length and
breadth of the rectangle​

Answer 1

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Length= 12cm and breadth =8cm

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☆ To find:

• The length and breadth of the rectangle.

☆Given:

• The length of a rectangle is 4 cm more than its breadth.

• If the length is increased by 4 cm and breadth decreased by 2 cm ,the area remain the same as of that original rectangle

☆Assuming:

• Let the breadth be x

• Therefore, length = (4+x)

☆Formula:

• Area of rectangle = lb ( length × breadth)sq unit

☆Solution:

♡The area of original rectangle

$-> x(x + 4) = {x}^{2} + 4x$

♡The length of the rectangle when increased by 4 cm

$- > (x + 4) + 4 = x + 4 + 4 = x + 8$

♡The breadth of the rectangle when decreased by 2 cm

$- > x - 2$

♡The area of new rectangle

$- > (x - 2)(x + 8) \\ = > x(x + 8) - 2(x + 8) \\ = > {x}^{2} + 8x - 2x - 16 \\ = > {x}^{2} + 6x - 16$

♡ATQ

$- > {x}^{2} + 4x = {x}^{2} + 6x - 16 \\ = > {x ^{2} } - {x}^{2} + 4x - 6x = - 16 \\ = > - 2x = - 16 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = > x = \frac{ - 16}{ - 2} = 8 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

♡Therefore,

• The breadth of the rectangle = x= 8cm

• The length of the rectangle = (x+4)= 8+4=12cm

☆Hence :

Length is 12 cm and breadth is 8 cm.

☆Verification :

• The area of original rectangle = (12×8)=96cm²
• The area of new rectangle =( 12+4)(8-2)=16×6=96 cm²
• Hence ,proved

hope it helps... :)