Question

The area of a trapezium is 384cm². Its parallel sides are in the ratio3 : 5 and the perpendicular distance between them is 12 cm. Find the length of each of the parallel sides.​

Answer 1

Step-by-step explanation:

Given :

Area of Trapezium is 384 cm² .

Parallel sides of trapezium are in the ratio 3:5 .

Perpendicular distance / Height is 12 cm .

To Find :

Length of each parallel sides .

Solution :

$\longmapsto\tt{Let\:one\:parallel\:side\:be=3x}$

$\longmapsto\tt{Let\:other\:parallel\:side\:be=5x}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:sides)}\times{h}}$

Putting Values :

$\longmapsto\tt{384=\dfrac{1}{{\cancel{2}}}\times{(3x+5x)}\times{{\cancel{12}}}}$

$\longmapsto\tt{384=(3x+5x)\times{6}}$

$\longmapsto\tt{384=18x+30x}$

$\longmapsto\tt{384=48\:x}$

$\longmapsto\tt{x=\cancel\dfrac{384}{48}}$

$\longmapsto\tt\bf{x=8}$

Value of x is 8 .

Therefore :

$\longmapsto\tt{Length\:of\:one\:parallel\:side=3(8)}$

$\longmapsto\tt\bf{24\:cm}$

$\longmapsto\tt{Length\:of\:other\:parallel\:side=5(8)}$

$\longmapsto\tt\bf{40\:cm}$

So , The Parallel sides of Trapezium are 24 cm and 40 cm .

Answer 2

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Given :-

Area of Trapezium is 384 cm² .

Parallel sides of trapezium are in the ratio 3:5 .

Perpendicular distance / Height is 12 cm .

To Find :-

Length of each parallel sides .

Solution :-

$\longmapsto\tt{Let\:one\:parallel\:side\:be=3x} \: \: \: \: </p><p>\longmapsto\tt{Let\:other\:parallel\:side\:be=5x}$

Using Formula :-

$\longmapsto\tt\boxed{Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:sides)}\times{h}}$

Putting Values :-

$\longmapsto\tt{384=\dfrac{1}{{\cancel{2}}}\times{(3x+5x)}\times{{\cancel{12}}}}⟼384=21×(3x+5x)×12</p><p>\longmapsto\tt{384=(3x+5x)\times{6}}⟼384=(3x+5x)×6</p><p>\longmapsto\tt{384=18x+30x}⟼384=18x+30x</p><p>\longmapsto\tt{384=48\:x}⟼384=48x</p><p>\longmapsto\tt{x=\cancel\dfrac{384}{48}}⟼x=48384</p><p>\longmapsto\tt\bf{x=8}⟼x=8$

Value of x is 8 .

Therefore :-

$\longmapsto\tt{Length\:of\:one\:parallel\:side=3(8)}⟼Lengthofoneparallelside=3(8)</p><p>\longmapsto\tt\bf{24\:cm}⟼24cm</p><p>\longmapsto\tt{Length\:of\:other\:parallel\:side=5(8)}⟼Lengthofotherparallelside=5(8)</p><p>\longmapsto\tt\bf{40\:cm}⟼40cm$

So , The Parallel sides of Trapezium are 24 cm and 40 cm