Question

The length of a rectangle is greater than the breadth by 3cm .If the length is increased by 9cm and the breadth is reduced by 5cm ,the area remains the same.Find the dimensions of the rectangle​

Answer 1

Given :-  

• Length of a rectangle is greater than the breadth by 3 cm  
• If the length is increased by 9cm and the breadth is reduced by 5cm ,the area remains the same .

To Find :-  

• Dimensions of the rectangle  

Solution :-  

❑  Let the breadth of the rectangle be ‘ x ‘  

Then length will be ‘ x + 3 ‘  

★ ATQ ::  

( x + 3 + 9 ) if the length is increased by 9 cm  

( x – 5 ) if the breadth is decreased by 5 cm  

*Area remains the same*

___________

$\sf {\dag} \;$  As we know that  ::

★ Area of Rectangle = lb  ★

Where ,  

• L is length  
• B is breadth  

___________  

Equation will be  

( x + 12 ) ( x – 5 ) = ( x ) ( x + 3 )  

___________

Let’s solve !  

➠ ( x + 12 )(x - 5) = ( x )( x + 3 )  

➠ x² + 7x − 60 = x( x + 3 )

~Use the distributive property to multiply x by  ( x +3 )

➠ x² + 7x − 60 = x² + 3x

~Subtract x² from both sides.

➠ x² + 7x  − 60 − x² = 3x

➠ 7x − 60 = 3x

➠ 7x − 60 − 3x=0

➠ 4x − 60 = 0

➠ 4x = 60

$\sf x = \dfrac{60}{4}$

$\sf \bigstar$  x = 15

Therefore :-  

✒ Length = ( x + 3 ) = ( 15 + 3 ) = 18 cm  

✒ Breadth = x = 15 cm  

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Answer 2

Answer:

Given :-  

Length of a rectangle is greater than the breadth by 3 cm  

If the length is increased by 9cm and the breadth is reduced by 5cm ,the area remains the same

.

To Find :-  

Dimensions of the rectangle  

Solution :-  

❑  Let the breadth of the rectangle be ‘ x ‘  

Then length will be ‘ x + 3 ‘  

★ ATQ ::  

( x + 3 + 9 ) if the length is increased by 9 cm  

( x – 5 ) if the breadth is decreased by 5 cm  

*Area remains the same*

___________

$\sf {\dag} \;$  As we know that  ::

★ Area of Rectangle = lb  ★

Where ,  

L is length  

B is breadth  

___________  

Equation will be  

( x + 12 ) ( x – 5 ) = ( x ) ( x + 3 )  

___________

Let’s solve !  

➠ ( x + 12 )(x - 5) = ( x )( x + 3 )  

➠ x² + 7x − 60 = x( x + 3 )

~Use the distributive property to multiply x by  ( x +3 )

➠ x² + 7x − 60 = x² + 3x

~Subtract x² from both sides.

➠ x² + 7x  − 60 − x² = 3x

➠ 7x − 60 = 3x

➠ 7x − 60 − 3x=0

➠ 4x − 60 = 0

➠ 4x = 60

$\sf x = \dfrac{60}{4}$

$\sf \bigstar$  x = 15

Therefore :-  

✒ Length = ( x + 3 ) = ( 15 + 3 ) = 18 cm  

✒ Breadth = x = 15 cm  

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Step-by-step explanation:

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