Question 209739
To solve the problem, we need to use the following formula:

{{{A = ((a+b)*h)/2}}}

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 = (x + x+2)*10/2}}}
Solving for x, we have
{{{150 = 5(2x+2)}}}
{{{150 = 10x + 10}}}

{{{140 = 10x}}}
{{{x=14}}}
So the shorter one is 14 meters long, the longer one is 16 meters long.