SOLUTION: A rectangular patio is 7 ft longer than it is wide. Determine the dimensions of the patio if it measures 13 ft diagonally.

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Question 198156: A rectangular patio is 7 ft longer than it is wide. Determine the dimensions of the patio if it measures 13 ft diagonally.
Answer by arallie(162) About Me  (Show Source):
You can put this solution on YOUR website!
Remember Rectangles have 4 90 degree angles 2 pair of equal and parallel sides, opposing each other. Also remember formulas for triangles. Splitting this rectangle will make things easier.
The width is simply "w".
Length is "7+w=l".
The hypotenuse is 13.
Pythagorean theorem.
a%5E2%2Bb%5E2=c%5E2 where a=w b=l and c=13
Since l=7+w we can substitute that value in b.
%28w%29%5E2%2B%287%2Bw%29%5E2=13%5E2
w%5E2%2B49%2B14w%2Bw%5E2=169
Put into quadratic form.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ where a=2 b=14 c=-120 x=w
2w%5E2%2B14w-120=0
w=%28-%2814%29%2B-sqrt%28%2814%29%5E2-4%282%29%28-120%29%29%29%2F%282%282%29%29+
w=%28-14%2B-sqrt%28196%2B960%29%29%2F4
w=%28-14%2B-34%29%2F4
Split
w=%28-14%2B34%29%2F4 w=%28-14-34%29%2F4
w=20%2F4 w=-48%2F4
w=5 w=-12
It only makes sense that w=5 is the only answer based on an inability to have a negative measurement. Substitute w=5 back into l=7+w to get l=12.
Answers
l=12ft w=5ft
P=34ft A=60sqft