Question

The length of one base of a trapezoid is 19 less than five times the length of the other base. If the trapezoid has a height of 18 feet an area of 477ft, find the length of the longer base

Answer 1

The length of the longer base is 41 ft.

Step-by-step explanation

Lets assume, length of one base is
`x` ft.

As, another base is 19 less than five times the length of this base, so the length of another base
`= (5x- 19) ft.`

The trapezoid has a height of 18 ft and area of 477 ft²

Formula for Area of trapezoid,
`A=(1)/(2) (a+b)*h` , where
`a, b` = Two bases of trapezoid and
`h` = height of the trapezoid.

Given in the question:
`A= 477` and
`h= 18`

We have also two bases as:
`a= x` and
`b= 5x-19`

So, according to the above formula...

`A= (1)/(2)(a+b)h\\\\ 477=(1)/(2)(x+5x-19)*18\\\\ 477=9(6x-19)\\\\477= 54x-171\\\\477+171=54x\\\\648=54x\\\\x=(648)/(54) = 12`

So, length of one base is
`12 ft` and another base
`=(5*12-19)ft =(60-19)ft = 41 ft`

That means, the length of the longer base is 41 ft.