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The perimeter of a rectangle is 70 cm. If its length is decreased by 5 cm and its width is increased by 5 cm, its area will increase by 50 cm2. Find the length and the width of the original rectangle.

Respuesta :

x=length of the original rectangle.  (in cm)
y=width o f the original rectangle.  (in cm)

Perimeter of a rectangle=sum of the all sides.
Perimeter of the original rectangle=x+x+y+y=2x+2y

Area of a rectangle=length x width
Area of the original rectangle=xy

x-5=length decreased by 5 cm
y+5=width increase by 5 cm.


We can suggest this system of equations:
  2x+2y=70
 (x-5)(y+5)=xy+50

We solve this system of equations by susbstitution method:
2x+2y=70  ⇒x+y=35  ⇒        y=35-x

(x-5)(35-x+5)=x(35-x)+50
(x-5)(40-x)=35x-x²+50
40x-x²-200+5x=35x-x²+50
40x-35x+5x=200+50
10x=250
x=250/10
x=25

y=35-x
y=35-25
y=10

Answer: the lenght and the width of the original rectangle is :
lenght=25 cm
width=10 cm.

The length of the rectangle is 25cm and the width of the rectangle is 45cm and this can be determine by forming the linear equations.

Given :

  • Perimeter of a rectangle is 70 cm.
  • Rectangle length is decreased by 5 cm and its width is increased by 5 cm, its area will increase by 50 [tex]\rm cm^2[/tex].

Let 'a' be the length of the rectangle and 'b' be the width of the rectangle. Than the perimrter of the rectangle will be:

a + b = 70  ---- (1)

Now, the area of the rectangle will be:

[tex]\rm (a-5)(35-a+5)=a(35-a)+50[/tex]

[tex]\rm 35a -a^2+5a-175+5a-25=35a-a^2+50[/tex]

[tex]\rm10a -200=50[/tex]

a = 25

Now, put the value of 'a' in equation (1).

b = 70 - 25 = 45

b = 45

Therefore, the length of the rectangle is 25cm and the width of the rectangle is 45cm.

For more information, refer the link given below:

https://brainly.com/question/919810

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