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The area of a trapezium is $$475 cm^2$$ and the height is 19 cm, then the lengths of smaller side of two parallel sides if one side is 4 cm greater than the other is 
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Solution

$$Let\quad the\quad length\quad of\quad one\quad parallel\quad side\quad of\quad trapezium\quad is\quad a.\\ So\quad length\quad of\quad other\quad parallel\quad side\quad =\quad a\quad +\quad 4\\ Given\quad the\quad area\quad of\quad trapezium\quad =\quad 475\quad \& \quad the\quad height\quad =\quad 19\\ Now\quad area\quad of\quad a\quad trapezium\quad =\quad \frac { 1 }{ 2 } \quad \times \quad height\quad \times \quad \left( sum\quad of\quad the\quad parallel\quad sides \right) \\ \Rightarrow \quad \frac { 1 }{ 2 } \quad \times \quad 19\quad \times \quad \left[ a\quad +\quad \left( a\quad +\quad 4 \right)  \right] \quad =\quad 475\\ \Rightarrow \quad 2a\quad +\quad 4\quad =\quad \frac { 475\quad \times \quad 2 }{ 19 } \\ \Rightarrow \quad 2a\quad +\quad 4\quad =\quad 25\quad \times \quad 2\\ \Rightarrow \quad 2a\quad +\quad 4\quad =\quad 50\\ \Rightarrow \quad 2a\quad =\quad 50\quad -\quad 4\\ \Rightarrow \quad 2a\quad =\quad 46\\ \Rightarrow \quad a\quad =\quad \frac { 46 }{ 2 } \quad =\quad 23\\ \therefore \quad Length\quad of\quad smaller\quad parallel\quad side\quad of\quad trapezium\quad =\quad 23\\ \& \quad Length\quad of\quad other\quad parallel\quad side\quad of\quad trapezium\quad =\quad 23\quad +\quad 4\quad =\quad 27$$

Mathematics

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