SOLUTION: The area of a rectangle is 344 cm sq. The height is three more than five times the base. What is the height?

Question 39728: The area of a rectangle is 344 cm sq. The height is three more than five times the base. What is the height?
Found 2 solutions by Fermat, smik:
Answer by Fermat(136) (Show Source): You can put this solution on YOUR website!
Let b = size of base
Let h = size of height
Let A = area
h = 3 + 5b (h is 3 more than 5 times base)
A = h * b
A = (3+5b)* b
344 = 3b + 5b�
5b� + 3b - 344 = 0
(5b + 43)(b - 8) = 0
b = -8.6, b = 8
Discarding the negative value,
b = 8
h = 3 + 5b
h = 3 + 40
h = 44
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Answer by smik(40) (Show Source): You can put this solution on YOUR website!
Very interesting question.

Okay, before jumping into the question let's translate the problem into some mathematical language.

We know that:

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.)

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:

344 = (3+5B) x B

Simplify this and we get:

344 = 3B + 5B^2

Simplify this further - since it's a quadratic equation - and we get:

0 = 5B^2 + 3B - 344

Now we can solve the equation using the Quadratic Equation Solver to get:

B = 8 or -8.6

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:

A = H x B
344 = H x 8 (divide both sides by 8)
H = 43

So the final answer is:

H = 43cm
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