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:
Let
Let
Let
Subtract fom both sides
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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:
The left side factors:
Setting each factor = 0 :
gives
gives
We discard the negative answer.
The width = =
The length = = =
Edwin