The length of the longer base is 41 ft.
Explanation
Lets assume, length of one base is [tex] x [/tex] ft.
As, another base is 19 less than five times the length of this base, so the length of another base [tex] = (5x- 19) ft. [/tex]
The trapezoid has a height of 18 ft and area of 477 ft²
Formula for Area of trapezoid, [tex] A=\frac{1}{2} (a+b)*h [/tex] , where [tex] a, b [/tex] = Two bases of trapezoid and [tex] h [/tex] = height of the trapezoid.
Given in the question: [tex] A= 477 [/tex] and [tex] h= 18 [/tex]
We have also two bases as: [tex] a= x [/tex] and [tex] b= 5x-19 [/tex]
So, according to the above formula...
[tex] A= \frac{1}{2}(a+b)h\\\\ 477=\frac{1}{2}(x+5x-19)*18\\\\ 477=9(6x-19)\\\\477= 54x-171\\\\477+171=54x\\\\648=54x\\\\x=\frac{648}{54} = 12 [/tex]
So, length of one base is [tex] 12 ft [/tex] and another base [tex] =(5*12-19)ft =(60-19)ft = 41 ft [/tex]
That means, the length of the longer base is 41 ft.
