Find the length of the bases

Question

The height of the trapezoid is 20ft and the area is 247ft²  

 

If one of the bases is 3 more than 6 times the other base, what are the lengths of the bases?

A= 1/2h(b+c)

Answer 1

Area = 1/2 * height * ( top + bottom)

 

The bases are the top and bottom of the trapezoid.

Bottom = 6 * Top + 3 <---- one of the bases is 3 more than 6 times the other

 

247 = 1/2 * 20 * (  Bottom + top    )

 

247 = 1/2 * 20 * ( 6 * top + 3   + top )

 

247 = 1/2 * 20 * ( 7 * top + 3)

 

247 = 10 * (7 * top + 3)

 

24.7 = 7 * top + 3

 

21.7 = 7  * top

 

top = 21.7/7 = 3.1

 

bottom = 6 * 3.1 + 3 

            = 18.6 + 3

            = 21.6

 

CHECK:   1/2 * 20 * ( 21.6 + 3.1)

               10 * (24.7) =

              247

 

the top is 3.1

the bottom is 24.7

Those are the lengths of the bases.

Answer 2

Let b = the shorter base

Let 6b + 3 = the longer base

247 = (1/2)(20)(b + 6b + 3)

247 = 10(7b + 3)

247 = 70b + 30

217 = 70b

3.1 feet = b

6(3.1) + 3 = 21.6 feet