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?


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 {{{243m^2}}}, then we'll have:  B(4B - 9) = 243

{{{4B^2 - 9B - 243 = 0}}}

(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 = {{{highlight_green(72)}}}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 {{{highlight_green(4)}}}m.