SOLUTION: The area of a rectangle is 338 mm2. The height is thirteen less than three times the base. What is the perimeter?

Question 1128052: The area of a rectangle is 338 mm2. The height is thirteen less than three times the base. What is the perimeter?
Found 3 solutions by Mtrkcrc, ikleyn, greenestamps:
Answer by Mtrkcrc(8)   (Show Source): You can put this solution on YOUR website!

then the base will be 13
the height will be 13*3-13
so the perimeter will be 13+13+13*3-13+13*3-13
which is 13*6
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

x*(3x - 13) = 338 3x^2 - 13x - 338 = 0 = = . Only positive root is meaningful: x = = 13. Thus the width is 13 mm; the length is 13*3 - 13 = 26 mm. The perimeter = 13 + 26 + 13 + 26 = 78 mm. ANSWER

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My understanding is that not only an answer does matter - the solution (I mean the correct and correctly presented solution) does matter, too.

It is why I wrote this post after the post by @Mtrkcrc.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The solutions by the other tutors using formal algebra are valid, and correct.

However, if speed in solving the problem is important and a formal algebraic solution is not required (as in a mathematics competition), take a few moments to see if the problem can be solved by logical guess-and-check, by assuming that the dimensions of the rectangle are "nice" numbers.

338 = 2*169 = 2*13*13

The most probable choice for the dimensions are then 13 and 26; and indeed 26 is 13 less than 3 times 13.

So the dimensions are 13 by 26, and the perimeter is 2(13+26) = 78.
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