document.write( "Question 1113959: A trapezoid of area 100 cm^2 has bases 5 cm and 15 cm. Find the areas of the two triangles formed by extending the legs until they intersect. \n" ); document.write( "

Algebra.Com's Answer #728998 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "We can find the height of the trapezoid, knowing its area and the lengths of its bases:
\n" ); document.write( " $\"100+=+%28%2815%2B5%29%2F2%29%2Ah\"$
\n" ); document.write( " $\"100+=+10h\"$
\n" ); document.write( " $\"h+=+10\"$

\n" ); document.write( "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).

\n" ); document.write( "Since the two triangles are similar, the ratio of their heights is the same as the ratio of their bases:
\n" ); document.write( " $\"x%2F%28x%2B10%29+=+5%2F15\"$
\n" ); document.write( " $\"5x%2B50=15x\"$
\n" ); document.write( " $\"10x=50\"$
\n" ); document.write( " $\"x=5\"$

\n" ); document.write( "So the small triangle has base 5 and height 5; its area is (1/2)(5)(5) = 25/2.

\n" ); document.write( "The large triangle has base 15 and height 10+5=15; its area is (1/2)(15)(15) = 225/2.
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