SOLUTION: O.K., I took a stab at this one and got to a dead end - any help getting through it would be greatly appreciated! A rectangular parking lot is 50ft. longer than it is wide. Det

Algebra ->  Linear-equations -> SOLUTION: O.K., I took a stab at this one and got to a dead end - any help getting through it would be greatly appreciated! A rectangular parking lot is 50ft. longer than it is wide. Det      Log On


   



Question 59264: O.K., I took a stab at this one and got to a dead end - any help getting through it would be greatly appreciated!
A rectangular parking lot is 50ft. longer than it is wide. Determine the dimentions of the parking lot if it measures 250ft. diagonally.
Thank you!

Found 2 solutions by josmiceli, Cintchr:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The therorem of Pythagoras says d%5E2+=+w%5E2+%2B+h%5E2
let x = h
x+50 = w
d = 250
%28x%2B50%29%5E2+%2B+x%5E2+=+250%5E2
2x%5E2+%2B+100x+%2B+2500+=+62500
2x%5E2+%2B+100x+-+60000+=+0
x%5E2+%2B+50x+-+30000+=+0
complete the square
x%5E2+%2B+50x+%2B+25%5E2+=+30000+%2B+25%5E2
%28x+%2B+25%29%5E2+=+30625
x+%2B+25+=+sqrt%2830625%29
x+%2B+25+=+175
x+=+150
x+%2B+50+=+200
so, h = 150 ft and w = 200 ft
check to see if the diagonal is 250 ft
%28x%2B50%29%5E2+%2B+x%5E2+=+250%5E2
200%5E2+%2B+150%5E2+=+250%5E2
40000+%2B+22500+=+62500
62500+=+62500
another check is, divide each dimension by 50
200%2F50+=+4
150%2F50+=+3
250%2F50+=+5
It's a 3-4-5 right triangle!

Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
For this you need the Pythagorean Theorum.
+a%5E2+%2B+b%5E2+=+c%5E2+
a = length (altitude) = b+50
b = width (base) = b
c - diagonal (hypotenuse) = 250
+a%5E2+%2B+b%5E2+=+c%5E2+
+%28b%2B50%29%5E2+%2B+b%5E2+=+250%5E2+
Foil the binomial
+b%5E2+%2B+100b+%2B+2500+%2B+b%5E2+=+250%5E2+
combine like terms
+2b%5E2+%2B+100b+%2B+2500+=+250%5E2+
Square the Hypotenuse
+2b%5E2+%2B+100b+%2B+2500+=+62500+
Move all values to the left side
+2b%5E2+%2B+100b+%2B+60000+=+0+
Divide all parts by 2
+b%5E2+%2B+50b+-+30000+=+0+
Factor
+%28b%2B200%29%28b-150%29+=+0+
set each piece equal to 0
+%28b%2B200%29=0 and %28b-150%29+=+0+
+b+=+-200+ and +b+=+150+
a Distance CAN NOT be a negative value.
+b+=+150+

Substitute
+a+=+b+%2B+50+
+a+=+150+%2B+50+
+a+=+200+

Dimentions:
Length = 200
Width = 150