SOLUTION: I need some help setting up these two questions as a quadratic equation that makes sense in the solution. Please help! A rectangular parking lot is 50 ft longer than it is wide

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Question 144908: I need some help setting up these two questions as a quadratic equation that makes sense in the solution. Please help!
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.



Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.

That says:

THIRD%5E2+=+SECOND%5E2%2B76

Let FIRST+=+x
Let SECOND+=+x%2B2
Let THIRD+=+x%2B4

%28x%2B4%29%5E2+=+%28x%2B2%29%5E2%2B76
%28x%2B4%29%28x%2B4%29+=+%28x%2B2%29%28x%2B2%29%2B76
x%5E2%2B4x%2B4x%2B16+=+x%5E2%2B2x%2B2x%2B4%2B76
x%5E2%2B8x%2B16=x%5E2%2B4x%2B80

Subtract x%5E2 fom both sides

8x%2B16=4x%2B80
4x=64
x=16

FIRST+=+x+=+16
SECOND+=+x%2B2+=+16%2B2+=+18
THIRD+=+x%2B4+=+16%2B4+=+20

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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. 




Let the width be w.

Since it is 50 ft longer than it is wide, 

the length is w+50

So we put w for the width, w+50 for the length,
and 250 for the diagonal.




Now let's take away the part above the diagonal:



That's just a right triangle and we can use
the Pythagorean theorem:

A%5E2%2BB%5E2=C%5E2

%28w%2B50%29%5E2%2Bw%5E2=250%5E2

%28w%2B50%29%28w%2B50%29%2Bw%5E2=62500

w%5E2%2B50w%2B50w%2B2500=62500

w%5E2%2B100w%2B2500=62500

w%5E2%2B100w-60000=0

The left side factors:

%28w%2B400%29%28w-150%29=0

Setting each factor = 0 :

w%2B400=0 gives w=-400

w%2B150=0 gives w=150

We discard the negative answer.

The width = w = 150ft

The length = w%2B50 = 150%2B50 = 200ft

Edwin