The length of one base of a trapezoid is 19 less than five times the length of the other base. of the trapezoid has a height of 18 feet and an area of 477ft^2, find the length of the longer base.

Let b1 represent the length of the first base, and b2 the length of the second one. Then we have ...

... b1 = -19 + 5b2 . . . . . . . . . . . . the relation between the base lengths

... Area = 1/2(b1 +b2)h . . . . . . . formula for area of a trapezoid

... 477 = (1/2)(b1 + b2)·18 . . . . . filling in the given values

Dividing the second equation by 9, we get

... b1 + b2 = 53

Subtracting b2, we get an expression for b1 that can be set equal to that given by the first equation.

... b1 = 53 - b2 = 5b2 -19

... 72 - b2 = 5b2 . . . . . . . . . add 19

... 72 = 6b2 . . . . . . . . . . . . . add b2

... 12 = b2 . . . . . . . . . . . . . . divide by 6

... b1 = 53 - 12 = 41 . . . . . . . from our second expression for b1

The longer base has length 41 feeet.

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