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

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) (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.
where a=w b=l and c=13
Since l=7+w we can substitute that value in b.

Put into quadratic form.
where a=2 b=14 c=-120 x=w

Split

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
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