Question

a field is in the form of a Trapezium its area is 1586 m square and the distance between its parallel sides is 26 m. if one of the parallel sides 84 M find the other

Answer 1

area of trapezium =1/2×sum of parallel side×distance between them
let the other parallel side be x

=1/2×(26+x)(26) =1586
=1/2×(26+x)=1586 /26
=1/2×(26+x)=61
=26+x=61×2
=26+x=122
=x=122-26
=x=96

therefore, other parallel side=96m

Answer 2

$\boxed{\boxed{\boxed{\bold{\green{solution :\longrightarrow }}}}}$

$\boxed{\boxed{\boxed{\bold{\blue{Given,}}}}}$

$\bold{Area \: \: of \: \: the \: \: trapezium = 1586 \: {m}^{2} }$

$\bold{Distance \: \: between \: \: them \: (h) = 26 \: m}$

$\bold{One \: \: parallel \: \: side = 84 \: m}$

$\bold\purple{Let \: \: the\:\:other \: \: parallel \: \: side \: \: be \: x \: m.}$

$\bold\pink{We \: \: know \: \: that}$

$\bold{Area \: \: o f \: \: trapezium = \frac{1}{2} \times (sum \: \: of \: \: || sides) \times h }\\ \\ \bold{= > 1586 = \frac{1}{2} \times (84 + x) \times 26 }\\ \\ \bold{= > 1586 = 13(84 + x)}$

$\bold{= > 1586 = 1092 + 13x} \\ \\\bold{ = >1586 - 1092 = 13x} \\ \\\bold{ = > 13x = 494} \\ \\\bold{ = > x = \frac{494}{13}} \\ \\ \bold{= > x = 38}$

$\boxed{\boxed{\boxed{\bold{Hence, \: \: the \: \: other \: \: parallel \: \: side \: \: is \: \: 38 \: \: m.}}}}$

$\boxed{\boxed{\boxed{\mathfrak{\red{I \: \: \: hope \: \: \: \: it \: \: \: \: will \: \: \: help \: \: you}}}}}$