   SEARCH HOME Math Central Quandaries & Queries  Subject: Involving quadratic equation Name: Carol Who are you: Student To use the quadratic equation you need both the perimeter and area of a rectangle. On the problem I list below, I can't figure out how to get the perimeter because I only have the price, Help! "The area of a rectangular field is 1200m^2. Two parallel sides are fenced with aluminum at $20/m. The remaining two sides are fenced with steel at$10/m. The total cost of the fencing is \$2200." What is the length of each side fenced with aluminum and steel? Thank you Hi Carol.

Write out the question using variables and you'll see what you need.

Let a = the length of one side of aluminum
Let s = the length of one side of steel

Then the area is:
sa = 1200

The cost of the aluminum is (2)a(20) = 40a and the steel costs (2)s(10) = 20s. The total cost is:
40a + 20s = 2200

Now you have two equations with two unknowns. Use any of the usual techniques (such as the substitution or elimination method) for solving this system of simultaneous equations. You will need to factor the quadratic (or use the quadratic formula if you can't see how to factor it) and you will find that there are two answers to this question!

Hope this helps,
Stephen La Rocque.     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.