Question

The length of a rectangle exceeds its breadth by 7 cm if the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle find the length and the breadth of the original rectangle please solve this question step by step ​

Answer 1

$\bf{\huge{\underline{\boxed{\sf{\red{Answer:}}}}}}$

$\bf{\underline{\underline{\sf{\green{Given:}}}}}$

• The length of a rectangle exceeds its breadth by 7 cm
• If the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle

$\bf{\underline{\underline{\sf{\green{To\:find:}}}}}$

• Length of the original rectangle
• Breadth of the original rectangle.

$\bf{\underline{\underline{\sf{\green{Solution:}}}}}$

Let the breadth of the rectangle be x cm.

$\bf{\underline{\underline{\sf{\pink{As\:per\:first\:condition:}}}}}$

• The length of a rectangle exceeds its breadth by 7 cm

Length of the rectangle = x + 7 cm

We know that the area of a rectangle is calculated using the formula,

$\bf{\large{\underline{\boxed{\sf{\purple{Area\:of\:a\:rectangle=\:length \times\:breadth}}}}}}$

Plug in the values,

=> Area = (x + 7) (x)

=> Area = x ( x + 7 )

=> Area = x² + 7x ---> 1

$\bf{\underline{\underline{\sf{\pink{As\:per\:second\:condition:}}}}}$

• If the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle

Length = x + 7 - 4 cm

Breadth = x + 3 cm

Since mentioned in the question, the area of both the rectangle, new as well as the original is same.

Area of rectangle = x² + 7x [from 1]

So using the formula for area of a rectangle and plugging the values,

=> Area = Length × Breadth

=> x² + 7x = (x + 7 - 4 ) ( x + 3)

=> x² + 7x = ( x + 3) ( x + 3)

=> x² + 7x = x ( x + 3) + 3 ( x + 3)

=> x² + 7x = x² + 3x + 3x + 9

=> x² + 7x = x² + 6x + 9

=> x² - x² + 7x - 6x = 9

=> 7x - 6x = 9

=> x = 9

$\bf{\large{\underline{\boxed{\sf{\orange{Breadth\:of\:the\:rectangle\:=\:x\:=\:9\:cm}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\orange{Length\:of\:the\:rectangle\:=\:x\:+\:7=\:9\:+\:7\:=16\:cm}}}}}}$

Answer 2

Answer:

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