Question

than the other, find the length
Open area of a house is in the shape of a trapezium with parallel sides in the ratio 3 : 5. Its area
50 m² and the perpendicular distance between the parallel sides is 5 metres. Find the length of the
parallel sides of that open area.
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Answer 1

Answer:

This is the answer for you are question

Answer 2

Step-by-step explanation:

$\frak {Given} \begin{cases} &\sf{Ratio\ of\ parallel\ sides\ of\ trapezium\ =\ 3\ :\ 5.} \\ &\sf{Area\ =\ 50m^2.} \\ &\sf{Perpendicular\ distance\ between\ the\ parallel\ sides\ =\ 5m.} \end{cases}$

To find:- Length of the parallel sides of trapezium ?

☯️ Let the sides of the trapezium be 3x and 5x.

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$\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}$

$\sf : \implies {Area\ of\ trapezium\ =\ \dfrac{1}{2}\ \times\ (Sum\ of\ parallel\ sides)\ \times\ (Distance\ between\ them).}$

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$\frak{\underline{\underline{\dag By\ substituting\ the\ values\ we\ get:-}}}$

$\sf : \implies {50\ =\ \dfrac{1}{2}\ \times\ (3x\ +\ 5x)\ \times\ 5} \\ \\ \\ \sf : \implies {50\ =\ \dfrac{1}{\cancel 2}\ \times\ 8x\ \times\ \cancel 5} \\ \\ \\ \sf : \implies {50\ =\ 2.5\ \times\ 8x} \\ \\ \\ \sf : \implies {\cancel \dfrac{50}{2.5}\ =\ 8x} \\ \\ \\ \sf : \implies {20\ =\ 8x} \\ \\ \\ \sf : \implies {\cancel \dfrac{20}{8}\ =\ x} \\ \\ \\ \sf : \implies {2.5\ =\ x} \\ \\ \\ \sf : \implies {\pink{\underline{\boxed{\bf x\ =\ 2.5}}}}\bigstar$

$\sf \therefore {\underline{Hence,\ the\ value\ of\ x\ is\ 2.5}}$

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$\frak{\underline{\underline{\dag Now,\ finding\ the\ parallel\ sides:-}}}$

$\sf : \implies {3x\ =\ 3\ \times\ 2.5\ =\ 7.5m.}$

$\sf : \implies {5x\ =\ 5\ \times\ 2.5\ =\ 12.5m.}$

Hence:-

$\sf \therefore {\underline{The\ length\ of\ the\ required\ sides\ are\ 7.5m\ and\ 12.5m.}}$