The length of a rectangle is 5ft longer than twice the width. If the perimeter is 106ft, find the length and the width of the rectangle.
What we know:
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
P = 2L + 2W
106 = 2(W + 5) + 2W
106 = 4W + 10
96 = 4W
24 = width
To solve this problem, we can use the formula for the perimeter of a rectangle, which is:
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.