Question 162743: a.
A rectangular parking lot is 100 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 500 ft diagonally.
b.
Three consecutive odd integers are such that the square of the third is 264 more than the square of the second. Find the three integers.
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! (x+100)^2+x^2=500^2
x^2+200x+10,000+x^2=250,000
2x^2+200x+10,000-250,000=0
2x^2+200x-240,000=0
2(x^2+100x-120,000)=0
2(x-300)(x+400)=0
x-300=0
x=300 is the width.
300+100=400 is the length.
Proof:
400^2+300^2=250,000
160,000+90,000=250,000
250,000=250,000
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let x, x+2 & x+4 be the 3 integers.
(x+4)^2=(x+2)^2+264
x^2+8x+16=x^2+4x+4+264
8x-4x=264-16+4
4x=252
x=252/4
x=63 is the smallest integer.
61+2=65 for the middle integer.
61+4=67 is the largest integer.
Proof:
67^2=65^2+264
4,489=4,225+264
4,489=4,489
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