P = 2L + 2W
106 = 2(W + 5) + 2W
106 = 4W + 10
96 = 4W
24 = width
106 = 2(W + 5) + 2W
106 = 4W + 10
96 = 4W
24 = width
Length = 2X + 5
Width = X
Perimeter = 2L + 2W
106 = 2(2X + 5) + 2X
106 = 4X + 10 + 2X
106 - 10 = 6X
96 = 6X
96 = 6X
___ ___
6 6
16 = X
Now we know X is 16 (Width)
Let's substitute:
Width = 16
Length = 2X + 5
= 2(16) + 5
= 37
Double check answers:
Perimeter = 2L + 2W
106 = 2(37) + 2(16)
106 = 74 + 32
Perimeter = 2(length + width)
Given that the perimeter is 106ft, we can write the equation as:
106 = 2(length + width)
Now, let's represent the width of the rectangle as "w" and the length as "l".
We are also given that the length is 5ft longer than twice the width. So we can write the equation:
l = 2w + 5
Now we can substitute this value of the length into the perimeter equation:
106 = 2((2w + 5) + w)
Simplifying the equation:
106 = 2(3w + 5)
106 = 6w + 10
Rearranging the equation:
6w = 106 - 10
6w = 96
Dividing both sides by 6:
w = 16
Now, we can substitute this value of the width back into the equation for the length:
l = 2w + 5
l = 2(16) + 5
l = 37
Therefore, the width of the rectangle is 16ft and the length is 37ft.