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The longest side of a right triangle is 15 feet. The third side is 15 less than three times the shortest side. Find the length of the shortest side.

 Jan 27, 2020
 #1
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The shortest side is 9 feet.

 Jan 27, 2020
 #2
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Solve for S:
225 = S^2 + (3 S - 15)^2

225 = S^2 + (3 S - 15)^2 is equivalent to S^2 + (3 S - 15)^2 = 225:
S^2 + (3 S - 15)^2 = 225

Expand out terms of the left hand side:
10 S^2 - 90 S + 225 = 225

Divide both sides by 10:
S^2 - 9 S + 45/2 = 45/2

Subtract 45/2 from both sides:
S^2 - 9 S = 0

Factor S from the left hand side:
S (S - 9) = 0

Split into two equations:
S - 9 = 0 or S = 0

Add 9 to both sides:
 
S = 9 

 Jan 27, 2020

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