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 incr
ease by 50 cm2. Find the length and the width of the original rectangle.
1 answer:
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.
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