SOLUTION: Please help me solve this word problem: A carpenter needs to cut a brace to support a vertical wall stud. The brace should be 7 feet less than 3 times the length of the stud. If

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Question 131745: Please help me solve this word problem:
A carpenter needs to cut a brace to support a vertical wall stud. The brace should be 7 feet less than 3 times the length of the stud. If the brace will be anchored on the floor 15 feet away from the stud, how long should the brace be? (Hint: the brace is the hypotenuse.)
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
a^2+b^2=c^2
x^2+15^2=(3x-7)^2
x^2+225=9x^2-42x+49
9x^2-x^2-42x+49-225=0
8x^2-42x-176=0
2(4x^2-21x-88)=0
2(4x+11)(x-8)=0
x-8=0
x=8 answer.
3*8-7=24-7=17 feet for the brace.
proof:
8^2+15^2=(3*8-7)^2
64+225=(23-7)^2
289=17^2
289=289