Question 1113959
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We can find the height of the trapezoid, knowing its area and the lengths of its bases:
{{{100 = ((15+5)/2)*h}}}
{{{100 = 10h}}}
{{{h = 10}}}<br>
When the legs of the trapezoid are extended until they intersect, two similar triangles are formed, the small triangle with height x and the large triangle with height (10+x).<br>
Since the two triangles are similar, the ratio of their heights is the same as the ratio of their bases:
{{{x/(x+10) = 5/15}}}
{{{5x+50=15x}}}
{{{10x=50}}}
{{{x=5}}}<br>
So the small triangle has base 5 and height 5; its area is (1/2)(5)(5) = 25/2.<br>
The large triangle has base 15 and height 10+5=15; its area is (1/2)(15)(15) = 225/2.<br>