Question 209727
area of a rectangle is 243 m2. The height is nine less than 4 times the base. What is the perimeter?


Let base of rectangle be B


Since the height is nine less than 4 times the base, then the height is 4B - 9


Since its area = 243m^2, we will have: B(4B - 9) = 243


B(4B - 9) - 243 = 0


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


(4B + 27)(B - 9) = 0


Therefore, 4B = - 27, or, B = 9


We will ignore the negative value as measuremnets CANNOT be negative


This means that B, or base = 9 meters


Now, since base = 9 meters, then height = 4(9) - 9, or, 27


Since base = 9 meters, and height = 27 meters, then perimeter = 2B + 2H ------> 2(9) + 2(27) ------> 18 + 54 = ({{{highlight_green(72)}}} meters.