SOLUTION: the area of a trapezoid is 150 sq. meters. the height is 10 meters and one base is two meters longer than the other base. Find the length of each base. show all work.

Algebra ->  Algebra  -> Surface-area -> SOLUTION: the area of a trapezoid is 150 sq. meters. the height is 10 meters and one base is two meters longer than the other base. Find the length of each base. show all work.      Log On

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Question 209739: the area of a trapezoid is 150 sq. meters. the height is 10 meters and one base is two meters longer than the other base. Find the length of each base. show all work.
Answer by math problem solving(30) About Me  (Show Source):
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To solve the problem, we need to use the following formula:
A+=+%28%28a%2Bb%29%2Ah%29%2F2
where
A is the area of a trapezoid
a and b are the lengths of its two bases
h is the height
Let x be the shorter base.
Then the longer base is x+2
Substituting the following into the formula
a = x
b = x+2
A = 150
h = 10
we have
150+=+%28x+%2B+x%2B2%29%2A10%2F2
Solving for x, we have
150+=+5%282x%2B2%29
150+=+10x+%2B+10
140+=+10x
x=14
So the shorter one is 14 meters long, the longer one is 16 meters long.