Question 39728
Very interesting question.
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Okay, before jumping into the question let's translate the problem into some mathematical language.
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We know that:
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A = 344      (where A is Area in cm sq.)
A = H x B    (where H is the height, and B is the base.)
H = 3 + 5B   (the problem tells us that the height is 3 more than 5 times the           base.)
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Know that all of the above is clear, we can substitute H for (3 + 5B) and A for (344) in the equation A = H x B, and so we get:
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344 = (3+5B) x B
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Simplify this and we get:
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344 = 3B + 5B^2
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Simplify this further - since it's a quadratic equation - and we get:
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0 = 5B^2 + 3B - 344
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Now we can solve the equation using the Quadratic Equation Solver to get:
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B = 8 or -8.6
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Since we're dealing with a positive area we can eliminate -8.6, which leaves us with the length of B as 8cm. However, the question asks us to figure out the height so we must plug it in into our initial formula (A = H x B) to solve for H:
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A = H x B
344 = H x 8     (divide both sides by 8)
H = 43 
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So the final answer is:
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H = 43cm