SOLUTION: Solve the following using applications of polymomials. A rectangular parking lot is 50 ft. longer than it is wide. Determine the diminsions of the parking lot if it measures 25

Question 67852: Solve the following using applications of polymomials.
A rectangular parking lot is 50 ft. longer than it is wide. Determine the diminsions of the parking lot if it measures 250ft. diagonally.

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

Let x=width
Then x+50=length
We'll apply the Pythagorean Theorm for right triangles:
a^2+b^2=c^2
x^2+(x+50)^2=250^2 clear parens
x^2+x^2+100x+2500=62,500
2x^2+100x+2500=62,500 divide all terms by 2
x^2+50x+1250=31,250 subtract 31,250 from both sides
x^2+50x-30,000=0 This can be factored:
(x+200)(x-150)=0

x= -200 ft----------can't have negative lengths
and
x=150 ft ------------------------Width
x+50=200 ft----------------------Length

CK
150^2+200^2=250^2
22,500+40,000=62,500
62,500=62,500

Hope this helps---ptaylor

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