Question

the length of rectangle is grater than the breadth by 18 cm .if both length and breadth are increased by 6cm then area increase by 168 cm square find length and breadth one variable

Answer 1

Answer:

Breadth of the original rectangle is 2 cm

Length of the original rectangle is 18 cm.

Step-by-step explanation:

Let the breadth of the rectangle be a cm,

So the length of the rectangle should ( a + 18 ) cm , as it is 18 cm greater than the breadth of the rectangle.

We know( formula ),

Area of rectangle = length x breadth

On the basis of the formula given above : -

Area of the original rectangle = a( a + 18 ) cm^2

According to the question,

New length = ( a + 18 + 6 ) cm = ( a + 24 ) cm

New breadth = ( a + 6 ) cm

Now,

Area of the new rectangle = ( a + 24 )( a + 6 ) cm^2

It is given in the question, if both length and breadth are increased by 6cm then area increase by 168 cm^2.

So,

⇒ Original area + 168cm^2 = new area

= >  a( a + 18 ) cm^2 + 168cm^2 = ( a + 24 )( a + 6 ) cm

= >  a( a + 18 ) + 168 = ( a + 24 )( a + 6 )

= >  a^2 + 18a + 168 = a^2 + 6a + 24a + 144

= >  a^2 - a^2 + 168 - 144 = 30a - 18a

= >  24 = 12a

= >  24 / 12 = a

= >  2 = a

Therefore, the breadth of the original rectangle is 2 cm and length of the original rectangle is 20 m. ( a + 18 = 2 + 18 = 20 cm )