Expert: Steve Holleran - 9/18/2007

Question
I have the answer but can't get the equations that will get me to the same place.
1.  3 consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.

2.  A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 250 ft diagonally.

a^2 + b^2 = diagonal - that's right isn't it?  I am not getting the equation to work out, what am I missing?

Answer
Hello Kristin,

1.  Okay, call the three even integers x, x+2, x+4.

Then, you have :  (x+4)^2 = (x+2)^2 +76

               x^2 + 8x +16 = x^2 + 4x + 4 + 76

                     8x + 16 = 4x + 80


                     4x = 64   so x = 16


and the three are 16, 18, 20; and it checks: 20^2 = 400

18^2 = 324 + 76 = 400.


2.  I think here you just left out the square on the diagonal:

      x^2 + (x+50)^2 = 250^2

      x^2 + x^2 + 100x + 2500 = 62500

      2x^2 + 100x -60,000 = 0

divide by 2 :

        x^2 + 50x - 30,000 = 0 .  I got x = 150, so the dimensions are 150 ft by 200 ft.

Hope this helps,

Steve Holleran