SOLUTION: The length of the lower base of a trapezoid is 2 cm. longer than the length of the upper base and the height is 1 cm. longer than the length of the upper base, what are the dimens

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The length of the lower base of a trapezoid is 2 cm. longer than the length of the upper base and the height is 1 cm. longer than the length of the upper base, what are the dimens      Log On

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Question 1168285: The length of the lower base of a trapezoid is 2 cm. longer than the length of the upper base
and the height is 1 cm. longer than the length of the upper base, what are the dimensions of
the trapezoid if the area is 36cm 2 ?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Use the given information to write the area in terms of a single variable:

x = length of upper base
x+2 = length of lower base (2cm longer than the upper base)
x+1 = height (1cm longer than the upper base)

The area of a trapezoid is the average of the two bases, multiplied by the height.

%28%28%28x%29%2B%28x%2B2%29%29%2F2%29%2A%28x%2B1%29+=+36
%28x%2B1%29%5E2+=+36
x%2B1+=+6 [ignore the negative answer since it makes no sense in the problem]
x+=+5

ANSWERS: The bases are x=5cm and x+2=7cm; the height is x+1=6cm.

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the length of the upper base.


Then the length of the lower base is (x+2) cm, and the length of the height is (x+1) cm.


The equation for the area of the trapezoid is


    %281%2F2%29%2A%28x+%2B+%28x%2B2%29%29%2A%28x%2B1%29 = 36  cm^2,   or

    %28x%2B1%29%5E2 = 36,


which implies

    x + 1 = sqrt%2836%29 = 6,

    x     = 5.


ANSWER.  The upper base is 5 cm long;

         the lower base is 7 cm long;

         the altitude is  6 cm.

Solved.