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Isosceles trapezoid ABCD is shown with midsegment EF. If base BC = 22x, base AD = 17x + 12, and EF = 18.5x + 8, what is BC? Isosceles trapezoid A B C D is drawn with parallel bases A D and B C and midsegment E F. 22 37 44 58

Respuesta :

The value of the base BC is 44

How to determine the value

It is important to note that the non-parallel sides and the base angles of an isosceles trapezoid are congruent.

Then, from the information given, we have;

  • Base BC = 22x
  • AD = 17x + 12
  • EF = 18.5x + 8

This is expressed as;

EF = Base BC + Base AD/2

Substitute the values into the equation

18.5x + 8 = 22x +  17x + 12/2

cross multiply

2(18. 5x + 8) = 22x + 17x + 12

expand the bracket

37x + 16 = 39x + 12

collect like terms

37x - 39x = 12 - 16

subtract like terms

-2x = -4

x = 2

But BC = 22x = 22(2 ) = 44

Thus, the value of the base BC is 44

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