Question

The length of rectangle is 4 cm more than its breadth and it's diagonal is 4cm than length find length and breadth

Answer 1

Correct Question:

Length of rectangle is 4 cm more than its breadth and its diagonal is 4 cm more than its length.

To find

Length & breadth of rectangle.

Solution

Let the breadth of rectangle be b cm & length of rectangle be (b + 4) cm

So, diagonal = 4 + b + 4 cm = (8 + b) cm

As we know,

➛ Diagonal = √(length² + breadth²)

Putting values :

⇒ (8 + b) = √[(b + 4)² + b² ]

⇒ (8 + b) = √[b² + 8b + 16 + b²]

⇒ (8 + b) = √(2b² + 8b + 16)

⇒ (8 + b)² = √(2b² + 8b + 16)²

⇒ 64 + 16b + b² = 2b² + 8b + 16

⇒ 2b² + 8b + 16 = b² + 16b + 64

⇒ 2b² + 8b + 16 - b² - 16b - 64 = 0

⇒ b² - 8b - 48 = 0

⇒ b² - 12b + 4b - 48 = 0

⇒ b(b - 12) + 4(b - 12) = 0

⇒ (b + 4)(b - 12) = 0

⇒ b = -4 or, b = 12

As, breadth of rectangle can't be negative.

∴ Breadth = b = 12 cm

Now finding length of rectangle :

⇒ Length = b + 4

= 12 + 4

= 16 cm

Therefore,

Length & breadth of rectangle are 16 cm & 12 cm respectively.

Answer 2

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QUESTION :

The length of rectangle is 4 cm more than its breadth and it's diagonal is 4cm than length find length and breadth.....

SOLUTION ;

Let the breath of the rectangle be X cm.

=> Length of the rectangle = X + 4 cm.

=> Diagonal of rectangle = X + 8 cm

This forms a right angled triangle..

=> L ^ 2 + B ^ 2 = D ^ 2

=> 2 X ^ 2 + 8 X + 16 = X ^ 2 + 16 X + 64

=> X ^ 2 - 8 X - 48 = 0

=> X ^ 2 - 12 X + 4 X - 48 = 0

=> X ( X - 12 ) + 4 ( X - 12 ) = 0

=> ( X + 4 ) ( X - 12 ) = 0

Length can not be negative.

So, X = 12 cm.

Breadth = 12 cm.

Length = 12 + 4 = 16 cm....