Find the short base $ b $ of a trapezoid if long base $a = \frac{ 19 }{ 2 }$ and median $m = \frac{ 44 }{ 5 }$.
Answer
$b = \frac{ 81 }{ 10 }$
Explanation
To find short base $ b $ use formula:
$$ m = \frac{ a + b } { 2 } $$After substituting $ m = \frac{ 44 }{ 5 } $ and $ a = \frac{ 19 }{ 2 } $ we have:
$$ \frac{ 44 }{ 5 } = \frac{ \frac{ 19 }{ 2 } + b } { 2 } $$ $$ \frac{ 44 }{ 5 } \cdot 2 = \frac{ 19 }{ 2 } + b $$ $$ \frac{ 19 }{ 2 } + b = \frac{ 88 }{ 5 } $$ $$ b = \frac{ 88 }{ 5 } - \frac{ 19 }{ 2 } $$ $$ a = \frac{ 81 }{ 10 } $$This page was created using
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