Answer: 20
Step-by-step explanation:
P=2a+2b=2(a+b)
a1=a+2
b1=b+4
Pnew=2(a+2)+2(b+4)
Pnew=2a+2b+4+8
Pnew=2(a+b)+12
Pnew=2P-8
P+12=2P-8
12+8=2P-P
20=P
The original perimeter of the rectangle is 20.
Given
A square has its length and width increased by two feet and four feet respectively so that it is now a rectangle.
The perimeter of the new rectangle is eight feet less than twice the original perimeter.
The perimeter of the rectangle is equal to the 2 times sum of length and width of the rectangle.
Let the length of the rectangle be x and the width is y.
The length of the new rectangle is x +2.
The width of the new rectangle is y+4.
The perimeter of the rectangle is given by;
[tex]\rm Perimeter \ of \ rectangle = 2 (length+width)[/tex]
Therefore,
The perimeter of the new rectangle is;
[tex]\rm Perimeter \ of \ rectangle = 2 (length+width)\\\\\rm Perimeter \ of \ rectangle = 2( (x+2)+(y+4))\\\\\rm Perimeter \ of \ rectangle =2(x+2+y+4)\\\\\rm Perimeter \ of \ rectangle = 2 (x+y+6)\\\\\rm Perimeter \ of \ rectangle = 2 p+12\\\\Pnew=2P-8\\\\P+12=2P-8\\\\12+8=2P-P\\\\20=P\\\\p=20[/tex]
Hence, the original perimeter of the rectangle is 20.
To know more about the perimeter of the rectangle click the link given below.
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