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.

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.