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mrs_skeptik [129]
3 years ago
8

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
Mathematics
1 answer:
ycow [4]3 years ago
8 0

The length of the longer base is 41 ft.

<u><em>Explanation</em></u>

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=\frac{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= \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

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.



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