ExplanationConvert this word problem into two equations with two variables. “The length is two more than twice the width” can be written as:

\(L = 2W + 2\)

Since the area is 40 and area is equal to length × width:

\(LW = 40\)

Since the first equation is already solved for L, plug (2W + 2) in for L into the second equation:

\((2W + 2)W = 40\)

\(2W^2 + 2W = 40\)

Since this is now a quadratic (there are both a W2 and a W term), get all terms on one side to set the expression equal to zero:

\(2W^2 + 2W - 40 = 0\)

Simplify as much as possible—in this case, divide the entire equation by 2—before trying to factor:

\(W^2 + W - 20 = 0\)

\((W - 4)(W + 5) = 0\)

W = 4 or –5

Since a width cannot be negative, the width is equal to 4. Since LW is equal to 40, the length must be 10. Now use the equation for perimeter to solve:

Perimeter = 2L + 2W

Perimeter = 2(10) + 2(4)

Perimeter = 28

Note that it might have been possible for you to puzzle out that the sides were 4 and 10 just by trying values. However, if you did this, you got lucky—no one said that the values even had to be integers!

_________________

Sandy

If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test