SOLUTION: An aluminum brace used to support a wooden shelf has a length that is 3 inches more than twice the width of the shelf. The brace is anchored to the wall h inches below the shelf. F
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Question 1162374: An aluminum brace used to support a wooden shelf has a length that is 3 inches more than twice the width of the shelf. The brace is anchored to the wall h inches below the shelf. Find the width of the shelf and the length of the brace. (Assume h = 12.)
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A step by step guide on figuring this out would be much appreciated. You don't have to give me the solution to this particular question but if you substitute the numbers to some other number and do a step by step guide that would be helpful. I'll be able to learn from that. Thank you!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let 
represent the width of the shelf and then 
must represent the length of the brace. Assuming that the shelf is exactly perpendicular to the wall, the line segment represented by 
, the brace, and the shelf form a right triangle where the brace is the hypotenuse. Hence,
^2\ =\ x^2\ +\ 12^2)
Expand
Collect like terms in the LHS:
Divide by the lead coefficient:
Factor
(x\ +\ 9)\ =\ 0)
So either 
or 
. Since a negative number for the width of anything is absurd, discard the negative root. That means , and therefore the brace is \ +\ 3\ = 13)
Check the work.
, 
, 
, and 
-- Checks.
Many thanks to Mr. Pythagoras.
John
My calculator said it, I believe it, that settles it
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