Answer:
Square:
s = 50 cm
Rectangle:
l = 60 cm
w = 40 cm
Let s be the side of a square.
We will be using the formula of Perimeter for square which states that
[tex]P=4s[/tex]Where:
P = Perimeter
s = side
Given a perimeter of 200 cm, we will substitute this value to the formula, and then solve for s.
[tex]P=4s[/tex][tex]200=4s[/tex]*Divide both sides by 4
[tex]\frac{200}{4}=\frac{4s}{4}[/tex][tex]s=50[/tex]Since we let s be the side of the square, the side of the square measures 50 centimeters.
To find the sides of the rectangle, we will use the following formula for the Perimeter of the Rectangle
[tex]P=2(l+w)[/tex]Where:
P = Perimeter
l = length
w = width
From the given, we have the following:
P = 200 cm
l = s + 10
w = s - 10
Substitute these to the formula, solve for s, and then use s to find the sides of the rectangle
[tex]P=2(l+w)[/tex][tex]200=2((s+10)+(s-10))[/tex][tex]200=2(s+10+s-10)[/tex][tex]200=2(s+s)[/tex][tex]200=2(2s)[/tex][tex]200=4s[/tex]*Divide both sides by 4
[tex]\frac{200}{4}=\frac{4s}{4}[/tex][tex]s=50[/tex]Now that we have a value of s, we will go back to our given to solve for the length and width of the rectangle
[tex]l=s+10[/tex][tex]l=(50)+10[/tex][tex]l=60[/tex][tex]w=s-10[/tex][tex]w=(50)-10[/tex][tex]w=40[/tex]The length of the rectangle would be 60 centimeters
The width of the rectangle is 40 centimeters
