SOLUTION: if a gate is "n" high and "2n" wide and the diagonal measures 96", what are the height and width of the gate?

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Question 1001777: if a gate is "n" high and "2n" wide and the diagonal measures 96", what are the height and width of the gate?
Found 3 solutions by vleith, addingup, Boreal:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Let's assume the gate is a rectangle.
Use Pythagorean theorem
n%5E2+%2B%282n%29%5E2+=+96%5E2
n%5E2+%2B+4n%5E2+=+9216
5n%5E2+=+9216
n%5E2+=+1843.2
n+=+42.93 inches
The gate is approximately 42.93 inches by 85.86 inches

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
Pythagoras:
a^2+b^2= c^2
---------------
n= 43 is your width
2n= 43*2=86 is your length

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
This is the Pythagorean Theorem
one side n
other side 2n
diagonal is 96
square them n^2+(2n)^2=96^2
5n^2=9216
n^2=1843.2
n=42.93 inches high
2n=85.86 inches wide