math problems

Question

A trapezoid is a four-sided figure with two of the sides, called the bases of the trapezoid, parallel to each other. If the lengths of the two bases are b1 and b2, and the distance between the bases is h, then the area of the trapezoid is given by the formula A=h(b1+b2)/2. for a particular trapezoid, the value of h is 5 feet, and the length of the longer base is 2 feet more than the length of the shorter base. If the area of the trapezoid is 45 square feet, find the lengths of the two bases of the trapezoid.

Answer 1

Let b₁ = smaller base

 

Then, b₂ = longer base = b₁ + 2

 

A = h(b₁ + b₂)/2 = h(b₁ + b₁ + 2)/2 = 45

 

                           5(2b₁ + 2)/2 = 45

 

                                b₁ + 1 = 9

 

                                       b₁ = 8    b₂ = b₁ + 2 = 10

 

                                    

The bases have lengths 8 ft and 10 ft.  

 

 

 

 

Answer 2

A = h(b₁ + b₂) / 2            substitute given values

45 = 5(2 + b₂) / 2            divide both sides by 5

9 = (2 + b₂) / 2                multiply both sides by 2

18 = 2 + b₂                      subtract 2 form both sides

16 = b₂

 

The second base is 16 feet.