Question

Length of a rectangle is 20 cm and its breadth is 4 cm. When a new rectangle is formed by changing the length and breadth, its perimeter decreased by 8 cm and area increased by 16 sq.cm. Find the change in its length and breadth ,

Answer 1

Answer:

12,8

Step-by-step explanation:

Length = 20

Breadth = 4

Perimeter = 2(L+B) = 2*24 = 48

Area = 20*4 = 80

New Perimeter = 48-8 = 40

New area = 80+16 = 96

If the new length is x, the new breadth will be (40-2x)/2 = 20-x

so x(20-x) = 96

x will be 8

so the new length and breadth will be 12 and 8

Answer 2

GIVEN :-

• Length of the original rectangle is 20 cm and its breadth is 4 cm .

• A new rectangle is formed by changing the length and breadth .

• Perimeter of the new rectangle is decreased by 8 cm .

• Area of the new rectangle is increased by 16 cm² .

TO FIND :-

• Change in its length and breadth .

SOLUTION :-

    Perimeter of the original rectangle = 2 ( 20 + 4 )

                                                               = 2 × 24

                                                               =  48 cm

        Area of the original rectangle = 20 × 4

                                                          = 80 cm²

Let the length and breadth be decreased by x and y respectively .

• Perimeter of the new rectangle is ,

                        $\longrightarrow\sf 2(20-x+4-y)=48-8\\\\\longrightarrow 2 \times (24-x-y)=40\\\\\longrightarrow 24-x-y =20\\\\\longrightarrow x+y = 4 \\\\\longrightarrow y = 4-x \ \ \ \ \ \ \ \ \ \ \ \ \ ........(1)$

• Area of the new rectangle is ,

                        $\longrightarrow \sf (20-x)(4-y)=80+16\\\\\longrightarrow 80-20y-4x+xy = 96 \\\\\longrightarrow xy-4x-20y = 16 \ \ \ \ \ \ \ \ \ \ \ \ ..................(2)$

  Put $\sf y=4-x$ in Eq (2) ,

                  $\longrightarrow \sf x(4-x)-4x-20(4-x)=16\\\\\longrightarrow 4x-x^2-4x-80+20x=16 \\\\\longrightarrow x^2-20x+96 =0 \\\\\longrightarrow x^2-12x-8x+96 = 0 \\\\\longrightarrow x(x-12)-8(x-12)=0\\\\\longrightarrow (x-12)(x-8)=0\\\\\longrightarrow \bf x = 12 \ , \ x=8$

• If x = 12 , y = 4 - 12 = -8

• If x = 8 , y = 8 - 12 = -4

If length is decreased by 12 cm , breadth is increased by 8 cm .

If length  is decreased by 8 cm , breadth is increased by 4 cm .

The new dimensions of the rectangle are 12 cm and 8 cm.