Question

the length of rectangle is 4 more than its breadth area is 140sq.cm calculate length and breadth

Answer 1

Length = 14 cm .

Breadth = 10 cm .

Given :-

• Length of rectangle is 4 more than its breadth . i,e. Length = 4 + breadth .
• Area of Rectangle = 140 cm² .

To find :-

• Length and Breadth of the rectangle .

Formula used :-

• Area of rectangle = Length × Breadth .

Solution :-

• Let Breadth of rectangle = x cm .

So, Length of rectangle = x + 4 cm .

Area of Rectangle = 140 cm² .

A.T.Q.

⟼ 140 = ( x + 4 ) × x

⟼ 140 = x² + 4x

⟼ x² + 4x – 140 = 0

( Splitting the middle term )

⟼ x² + ( 14 – 10 )x – 140 = 0

⟼ x² + 14x – 10x – 140 = 0

⟼ x( x + 14 ) – 10( x + 14 ) = 0

⟼ ( x + 14 ) ( x – 10 ) = 0

x + 14 = 0 x – 10 = 0

x = – 14 x = 10

Here, we have two values of x ( Breadth ) first is –14 which is not possible because x determines the Breadth of the rectangle and Breadth of rectangle never be in negative . So, Breadth = 10 cm .

Now, Length of rectangle = Breadth + 4

⟼ = 10 + 4

⟼ = 14 cm

Hence required Length and Breadth of the rectangle are 14 cm and 10 cm respectively .

Properties of Rectangle .

• Rectangle have 4 angles and all angles are of 90° .
• Rectangle have 2 diagonals and both diagonals are equal .
• The diagonals of rectangle bisect each other .
• Opposite sides of Rectangle are equal and parallel.
• Rectangle can be Parallelogram .

Formula related to Rectangle

• Perimeter of Rectangle = 2( L + B ) . where L = Length and B = Breadth .
• Area of Rectangle = L × B .
• Diagonal of Rectangle = √[(Base)² = (Height)²] .

Answer 2

Given: the length of rectangle is 4 cm more than its breadth

area is 140 sq.cm  

To Find: length and breadth

Solution:

length of rectangle is 4 cm more than its breadth

Breadth = x   cm

Length = x + 4 cm

Area of a rectangle = length * breadth

=> Area of the rectangle =  (x + 4)x   cm²

Area of the rectangle =  140  cm²

Equate Area

=>   (x + 4)x   = 140

=> x² + 4x - 140 = 0

Using middle term split

=> x² + 14x - 10x - 140 = 0

=> x( x+ 14) - 10(x + 14) = 0

=> (x + 14)(x - 10) = 0

=> x = - 14 , x = 10

Length can not be negative

Hence x = 10

Breadth = 10 cm

Length = 14 cm

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