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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

1 Answer

4 votes

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.



User Toby Mellor
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