Question

The parallel sides of a trapezium are in the ratio 6:7 and the distance between them is 12.5cm find the length of sides if the area is 6.50

Answer 1

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

$\sf \implies 4800cm \:and \:5600cm$

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

$\bold{Given}\begin{cases}\sf{Area\:of\: trapezium=6.50m{}^{2}}\\ \sf{Parallel\:sides\:in\:ratio=6:7}\\ \sf{Height=12.5cm}\end{cases}$

$\sf Area\:in\:cm{}^{2}=6.50×10000\\ \\ \sf\implies Area=65000cm{}^{2}$

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

• Let the parallel sides be x
• 6x and 7x

$\sf Area=\frac{1}{2}\times h\times (Sum\:of\: parallel\:sides)\\ \\ \sf\leadsto 65000=\frac{1}{\cancel2}\times \cancel{12.5}\times (6x+7x)\\ \\ \sf\leadsto 65000 =6.25\times 13x\\ \\ \sf\leadsto \cancel{\frac{65000}{6.25}}=13x\\ \\ \sf\leadsto 10400=13x\\ \\ \sf\leadsto \cancel{\frac{10400}{13}}=x\\ \\ \sf\implies x=800$

• The value of x is 800

Now we write the parallel sides in 6x and 7x

• SO,the value of x is 800

$\sf\ 6x=6×800\\ \\ \sf\implies 4800$

$\sf 7x=7×800=5600$

The parallel sides of trapezium is 4800 and 5600

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