The perimeter of a rectangle is 85 feet. The length of the rectangle is , 2, ( x + 16 ), and the width is , 3x minus 1, . What is the length of the rectangle?

We know that for a rectangle of length L and width W, the perimeter is:

P = 2*L + 2*W.

In this case, we know that:

P = 85ft = 2*L + 2*W

L = 2*(x + 16)

W = (3*x - 1)

(where i guess that these units are in ft )

This is a system of equations:

Then we can replace the second and third equation into the first one, and get:

85 = 2*2*(x + 16) + 2*(3x - 1)

And solve this for x, we will get:

85 = 4x + 64 + 6x - 2

85 - 64 + 2 = (4 + 6)*x

23 = 10*x

23/10 = x

2.3 = x

Then the measures of the rectangle are:

L = 2*(x + 16) = 2*(2.3 + 16) = 36.6

W = (3*x - 1) = (3*2.3 - 1) = 5.9

The length of the rectangle is 36.6 feet, (and the width is 5.9 feet)