Question

their area of a Trapezium is 78 CM square and its height is 13 cm if one of the parallel side is longer than the other by 2 cm find the length of two parallel side​

Answer 1

$\huge\mathtt{\underline{ANSWER:-}}$

$\sf\implies 5cm\:and\:7cm$

$\huge\mathbb{\underline{\underline{SOLUTION:-}}}$

$\bold{Given}\begin{cases}\sf{Area\:of\: trapezium=78cm{}^{2}}\\ \sf{Height=13cm}\end{cases}$

$\huge\sf {To\:Find}$

• The length of two parallel sides

$\bold{\underline{\underline{According\:to\: question:-}}}$

• Let it's parallel side be x

• and rhe other is x+2

$\mathfrak {\underline{Area\:of\: trapezium=\frac{1}{2}\times Height\times (sum\:of\: parallel\:sides}}$

$\sf Area=\frac{1}{2}\times H\times sum\:of\: parallel\:sides\\ \\ \sf\implies 78=\frac{1}{2}\times 13\times x+x+2\\ \\ \sf\implies 78\times 2=13\times 2x+2\\ \\ \sf\implies \frac{\cancel156}{\cancel13}=2x+2\\ \\ \sf\implies 12-2=2x\\ \\ \sf\implies \frac{\cancel{10}}{\cancel2}=x\\ \\ \sf\implies x=5$

• One of its parallel side is 5cm

• and the other is greater by 2 cm
• then the other side is 5+2 7cm

• The parallel sides of trapezium area 5cm and 7cm

$\mathfrak{\underline {\purple{Verification:-}}}$

$\bold{We\: find}\begin{cases}\sf{Area\:of\: trapezium=78cm{}^{2}}\\ \sf{Height=13cm}\\ \sf{Parallel\: sides=5cm\:and\:7cm}\end{cases}$

$\sf Area\:of\: trapezium=\frac{1}{2}\times h\times (sum\:of\: parallel\:sides)\\ \\ \sf\leadsto 78cm{}^{2}=\frac{1}{2}\times 13cm\times (7+2)cm\\ \\ \sf\leadsto 78cm{}^{2}=\frac{1}{\cancel2}\times 13cm\times \cancel{12}cm\\ \\ \sf\leadsto 78cm{}^{2}=13cm\times 6cm\\ \\ \sf\leadsto 78cm{}^{2}=78cm{}^{2}\\ \\ \sf L.H.S=R.H.S$

$\boxed{\underline{Parallel\:sides=5cm\:and\:7cm}}$

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Answer 2

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