SOLUTION: The area of a square is one third as large as the area of a triangle. One side of the triangle is 9 inches long and the altirude to that side is the same length as a side of the sq

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Question 175457: The area of a square is one third as large as the area of a triangle. One side of the triangle is 9 inches long and the altirude to that side is the same length as a side of the square. What is the length of the side of the square. What is the formula for this word problem?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let s= a sides of the square
Let A%5Bs%5D = area of square
A%5Bs%5D+=+s%5E2
---------------
For triangle:
A%5Bt%5D+=+%281%2F2%29%2Ab%2Ah
It is given that h+=+s
and b+=+9in
A%5Bt%5D+=+%281%2F2%29%2As+%2A9
A%5Bt%5D+=+%289%2F2%29%2As
------------
Also given is:
A%5Bs%5D+=+%281%2F3%29%2AA%5Bt%5D
therefore:
s%5E2+=+%281%2F3%29%2A%289%2F2%29%2As
Multiply both sides by 6
6s%5E2+=+9s
6s%5E2+-+9s+=+0
s%286s+-+9%29+=+0
The solutions are:
s+=+0 This one doesn't work here
s+=+3%2F2
The side of the square is 1.5 in
check:
A%5Bs%5D+=+s%5E2
A%5Bs%5D+=+2.25
A%5Bt%5D+=+%289%2F2%29%2As
A%5Bt%5D+=+6.75
Also given is:
A%5Bs%5D+=+%281%2F3%29%2AA%5Bt%5D
2.25+=+%281%2F3%29%2A6.75
6.75+=+6.75
OK