Length of a rectangle is 6 …

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Length of a rectangle is 6 cm more than its width.If it's length and breadth each is decreased by 3cm the area of new rectangle is decreased by 36 Sq cm.Find the original length and breadth of the original rectangle.

Posted by Yash Thadani 6 years, 11 months ago

CBSE > Class 08 > Mathematics

1 answers

Rupender Singh 6 years, 11 months ago

Let the original Breadth of rectanlge be = x cm

and the original Length of rectangle be = (x + 6) cm

Therefore, Original Area = Length × Breadth = (x + 6) × x = x² + 6x

Now, New Length = (x + 6) - 3 = x + 6 - 3 = x + 3

New Breadth = x - 3

Therefore, New Area = Length × Breadth = (x + 3) × (x - 3) = (x)² - (3)² = x² - 9

According to Question

Original Area - New Area = 36 sq cm.

(x² + 6x) - (x² - 9) = 36

x² + 6x - x² + 9 = 36

6x + 9 = 36

6x = 36 - 9

6x = 27

x = {tex}{27\over6} = {9\over2}{/tex}

Hence, Original Length of Rectangle = x + 6 = {tex}{9\over 2} + 6 = {9 + 12\over 2} = {21\over 2} = 10.5{/tex}cm

Original Breadht of Rectangle = x = {tex}{9\over 2} = 4.5{/tex} cm

1Thank You

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