Question

The length of a rectangle is 5 less than twice the width. If the perimeter of the rectangle is 146 centimeters, find the dimensions of the rectangle.

Answer 1

Length of rectangle = 5 less than 2x width
Perimeter = 146 cm

Equations we will use...
w = width
(2w - 5) = length (l)
perimeter (p) = 2(l + w)

Substitute equation for length into equation for perimeter
p = 2(l + w)
146 = 2((2w - 5) + w)     [use distributive prop.]
146 = 4w - 10 + 2w        [combine like terms]
146 = 6w -10                  [solve for w]
156 = 6w
w = 26 cm

Now substitute width back into the equation for length...
l = 2w - 5
l = 2(26) - 5
l = 47

Double check to make sure values added up to 146 cm
w + w + l + l = 146
26 + 26 + 47 + 47 = 146
146 = 146

Therefore, the width is 26 cm and the length is 47 cm.