Question 534102: Please help me solve this problem I am completely lost on both the setup and solving: Joe Schmoo just moved into a new house where the living room is a square whose diagonal is 7 feet longer that the length of a side. Find the dimensions of the living room.
Answer by fcabanski(1391)   (Show Source):
You can put this solution on YOUR website! Call the side of the square (living room) S.
The diagonal, D, is 7 feet longer than the length of a side. Thus:
D = S+7
We also know a relationship between the diagonal of a square and the sides, thanks to the Pythagorean Theorem. In simple form it's the formula for the diagonal of a square:
d = sqrt(2)*s in our case D = sqrt(2)*S
In our case we have two equations, and two unknowns. We can easily solve for both unknowns. And we already have D expressed as S. We can substitute that (S+7) in for D in the diagonal formula.
S+7 = sqrt(2)*S Subtract S from both sides.
7 = SQRT(2)*S - S = S *((sqrt(2)-1)
Divide both sides by sqrt(2)-1
7/(sqrt(2)-1) = S = approximately 17
The room is a square with sides length 17 (approximately).
It is exactly a square with sides 7/(sqrt(2)-1)
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