Question 209335: What is the perimeter of a rectangle when the area is 243m squared and the height is nine less than four times the base?
What is the height of a a rectangle if the perimeter is 40m and the base is four less than five times the height?
Found 2 solutions by rfer, MathTherapy:
Answer by rfer(16322)   (Show Source):
Answer by MathTherapy(10555)  (Show Source):
You can put this solution on YOUR website! What is the perimeter of a rectangle when the area is 243m squared and the height is nine less than four times the base?
What is the height of a a rectangle if the perimeter is 40m and the base is four less than five times the height?
a)
Let the base of the rectangle be B
Since its height is nine less than four times the base, then its height is 4B - 9
Since its area is  , then we'll have: B(4B - 9) = 243
(4B + 27)(B - 9) (Factoring quadratic equation)
Therefore, (4B + 27) = 0, or (B - 9) = 0, but since 4B + 27 = 0 will result in a negative number, we ignore becuase a measurement CANNOT be negative
Therefore, B - 9 = 0, and B = 9
Now, since B, or base = 9, height = 4B - 9, or 4(9) - 9 = 36 - 9 = 27
The perimeter of this rectangle will then be: 2(9) + 2(27) = 18 + 54 =  m.
b)
Let height be H
Since its base is four less than five times the height, then its base = 5H - 4
Since its perimeter is 40m, then we have:
2H + 2(5H - 4) = 40
2H + 10H - 8 = 40
12H = 48
H = 4
Therefore, the height is  m.
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