Question

The area of a trapezium is 180cm^2and it's height is 12cm .if one of the parallel sides is double the other, find the length of the parallel sides.

Answer 1

let one of the parallel side be x cm
therefore, the other parallel side = 2x cm

area of trapezium = 180cm²
=> 1/2 (sum of parallel sides)h = 180
=>1/2(2x+x)12 = 180
=> 6(3x) = 180
=> 18x=180
=>x = 180/18
=>x= 10

so, one of the parallel side=10cm
other parallel side= 2(10)= 20cm

Answer 2

AnswEr

$\frak{Given}\begin{cases}\sf{Area \ of \ the \ trapezium = 180 \ cm^2}\\\sf{Height \ of \ the \ trapezium = 12 \ cm}\\\sf{One \ || \ side \ is \ double \ the \ other \ side}\end{cases}$

Let's consider that first side of the trapezium be x cm & second side be 2x cm.

By using Trapezium Formula,

$\star\ \boxed{\sf{\purple{Area_{(Trapezium)} = \frac{1}{2} \times (Sum \ of \ || \ sides) \times (Height)}}}$

☯ Substituting the Given values

$:\implies\sf 180 = \dfrac{1}{2} \times (x + 2x) \times 12 \\\\\\:\implies\sf 180 = \dfrac{1}{\cancel{\: 2}} \times 3x \times \cancel{12} \\\\\\:\implies\sf 180 = 3x \times 6\\\\\\:\implies\sf 180 = 18x \\\\\\:\implies\sf x = \cancel\dfrac{180}{18}\\\\\\:\implies\boxed{\frak{\pink{\: x = 10 cm \: }}}$

$\bigstar$ The Length of the || sides are :

• First side, x = 10 cm
• Second side, 2x = 20 cm