Question 105084
Let L = the length and W = the width.
From the problem description, you can write:
L = 5W+2 "The length (L) of the rectangle is (=) 2 more (+2) than 5 times its width (5W)"
A = 65 sq.cm. "The area of the rectangle is 65 sq.cm."
The formula for the area of a rectangle is:
A = L*W  Make the appropriate substitutions.
{{{65 = (5W+2)*W}}} Simplify and solve for W.
{{{65 = 5W^2 + 2W}}} Subtract 65 from both sides.
{{{5W^2+2W-65 = 0}}} Use the quadratic formula to solve for W.
{{{W = (-2+-sqrt(2^2-4(5)(-65)))/2(5)}}}
{{{W = -3.811}}} Discard the negative solution.
{{{W = 3.411}}}
The width is 3.41 cm