Question

14. The length of a rectangle exceeds the breadth by 6 cm. If the length is increased by 3 cm
and breadth decreased by 2 cm, the area remains the same. Find the length and breadth of
the rectangle.
O Dil​

Answer 1

Answer:

Length is 24 cm and breadth is 18 cm.

Step-by-step explanation:

Let the breadth of the rectangle be a.

      According to the situation given :

Length of a rectangle exceeds the breadth by 6 cm, so if breadth is a then length should be a + 6.

Therefore area of the rectangle is a( a + 6 ).

 Given situation says is length is increased by 3 cm and breadth is decreased by 2 cm, area remains unchanged.

Now, length is a + 6 + 3 and breadth is a - 2.

Area ( with the changes in measures ) is ( a + 9 )( a - 2 )

Given,

    Area remains same, so

⇒ a( a + 6 ) = ( a + 9 )( a - 2 )

⇒ a^2 + 6a = a^2  - 2a + 9a - 18

⇒ 6a = 7a - 18

⇒ 18 = 7a - 6a

⇒ 18 = a

Therefore,

Length of the rectangle is a + 6 ⇒ 6 + 18 cm ⇒ 24 cm

Breadth of the rectangle is a ⇒ 18 cm

Answer 2

$\Large{\underline{\underline{\bf{Solution :}}}}$

___________________________

★ Given :

Length of rectangle is 6 cm more than its breadth.

If length is increased by 3 cm and breadth decreased by 2 cm.

___________________________

★ To Find :

We have to find the length and breadth of rectangle.

___________________________

★ Solution :

Let the breadth of rectangle be x.

So, Length of rectangle = (x + 6)

Now,

When Length is incresed and breadth is decreased.

We get

Length = (x + 6 + 3) = (x + 9)

Breadth = (x - 2)

$\rule{150}{2}$

Now,

$\sf{→ (x + 6)(x) = (x + 9)(x - 2)} \\ \\ \sf{→\cancel{x^2} + 6x = \cancel{x^2} - 2x + 9x - 18} \\ \\ \sf{→6x = 7x - 18} \\ \\ \sf{→7x - 6x = 18} \\ \\ \sf{→x = 18}$

Breadth = x = 18 cm

Now, Length = (x + 6) = (18 + 6) = 24 cm