Question

Length of a rectangle is 20 cm and its breadth is 4 cm. When a new rectangle is formed by changing its length and breadth its perimeter decreased by 8 cm and area increases by 16 Sq cm find the change in its length and breadth
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Answer 1

Step-by-step explanation:

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 ,

\begin{gathered}\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)\end{gathered}

⟶2(20−x+4−y)=48−8

⟶2×(24−x−y)=40

⟶24−x−y=20

⟶x+y=4

⟶y=4−x ........(1)

Area of the new rectangle is ,

\begin{gathered}\longrightarrow \sf (20-x)(4-y)=80+16\\\\\longrightarrow 80-20y-4x+xy = 96 \\\\\longrightarrow xy-4x-20y = 16 \ \ \ \ \ \ \ \ \ \ \ \ ..................(2)\end{gathered}

⟶(20−x)(4−y)=80+16

⟶80−20y−4x+xy=96

⟶xy−4x−20y=16 ..................(2)

Put \sf y=4-xy=4−x in Eq (2) ,

\begin{gathered}\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\end{gathered}

⟶x(4−x)−4x−20(4−x)=16

⟶4x−x

2

−4x−80+20x=16

⟶x

2

−20x+96=0

⟶x

2

−12x−8x+96=0

⟶x(x−12)−8(x−12)=0

⟶(x−12)(x−8)=0

⟶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.

Answer 2

Step-by-step explanation:

Let the length be l and breadth be b

Original area of the rectangle=l*b

Given l=b+4

When the length is increased by 4cm,new length=l+4

When the breadth is decreased by 2 cm ,new breadth=b-2

(l+4)(b-2)=lb [given the area remains same]

lb-2l+4b-8=lb

-2l+4b=8 [lb get cancelled on both sides]

-l+2b=4 [dividing by 2}

-b-4+2b=4 [l=b+4 therefore -l=-(b+4)=-b-4]

b=8 cm

l=4+8=12 cm

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