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

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

Answer:

24 cm and 40 cm

Step-by-step explanation:

let the parallel sides be 3x and 5x.

area of trapezium = (sum of parallel sides / 2)× perpendicular distance between parallel sides

therefore, ((3x + 5x)/2) × 12 = 384

(8x/2) × 12 = 384

4x = 384/12

4x = 32

x = 32/4

x = 8

therefore, the length of each parallel sides are

3x = 3(8) = 24 cm

and

5x = 5(8) = 40 cm