Given:
Length of the rectangle = x + 21
Width of the rectangle = 5
To find:
Perimeter and area of the rectangle
Solution:
Perimeter = [tex]2(l + w)[/tex]
[tex]=2(x+21+5)[/tex]
[tex]=2(x+26)[/tex]
Perimeter [tex]=2x+52[/tex] units
Area = length × width
[tex]=(x+21)\times 5[/tex]
Area [tex]=5x + 105[/tex] square units
Substitute perimeter is 100 and find the value of x:
[tex]100=2x+52[/tex]
Subtract 52 from both sides.
[tex]100-52=2x+52-52[/tex]
[tex]48=2x[/tex]
Divide by 2 on both sides, we get
[tex]24=x[/tex]
x = 24
Substitute area is 200 and find the value of x:
[tex]200=5x + 105[/tex]
Subtract 105 from both sides.
[tex]200-105=5x + 105-105[/tex]
[tex]95=5x[/tex]
Divide by 5 on both sides, we get
[tex]19=x[/tex]
x = 19
If the perimeter is 100, then the value of x is 24.
If the area is 200, then the value of x is 19.
