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 + 5bē
5bē + 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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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
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