SOLUTION: Two complementary angles have degree measures p and 3p - 6. Even integers. Find two consecutive even integers that have a sum of 450. The length of a rectangular lot is 50 fe

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Question 130734: Two complementary angles have degree measures p and 3p - 6.
Even integers. Find two consecutive even integers that have a sum of 450.
The length of a rectangular lot is 50 feet more than the width. If the perimeter is 500 feet, then what are the length and width?

Answer by solver91311(24713) About Me  (Show Source):
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Angles are complementary if and only if the sum of their measures is 90 degrees. If the two angles have degree measures of p and 3p - 6, then:

p+%2B+3p+-+6+=+90
4p-6=90
4p=96
p=24

Check:
3%2A24-6=72-6=66.
66%2B24=90 Answer checks.

If x is an even integer, the next consecutive even integer is x + 2 (that's because x + 1 would be odd). Their sum is 450, so x+%2B+%28x+%2B+2%29=450

2x%2B2=450
2x=448
x=224

Check:
224+%2B+226+=+450 Answer checks.

The perimeter of a rectangle is P=2L+%2B+2W, but we are given that L=W%2B50 and P=500, so:

2%28W%2B50%29%2B2W=500
2W%2B100%2B2W=500
4W%2B100=500
4W=400
W=100
L=W%2B50
L=150

Check:
P=2L%2B2W=2%28150%29%2B2%28100%29=300%2B200=500 Answer checks.