Question

trapezium is 180sq.cm and its height is 9cm. if one of the parallel sides is longer

than the other sides 6cm, find the length of parallel sides​

Answer 1

$\huge {\underline {\underline \pink{ƛƝƧƜЄƦ}}}$

Given

• Area of trapezium = 180 sq.cm
• Height = 9cm

To Calculate

• Length of parallel sides

Solution

Let one side be x

Other side = x + 6

Area of Trapezium

$\bf \implies \frac{1}{2} \times sum \: of \: ll \: sides \times h = 180 {cm}^{2}$

$\bf \implies \frac{1}{2} \times (x + x + 6) \times 9 = 180 {cm}^{2}$

$\bf \implies \frac{1}{2} \times (2x + 6) = 180 \div 9$

$\bf \implies \frac{1}{2} \times (2x + 6) = 20$

$\bf \implies 2x + 6 = 20 \times 2$

$\bf \implies 2x + 6 = 40$

$\bf \implies 2x = 40 - 6$

$\bf \implies 2x = 34$

$\bf \implies x = 34 \div 2$

$\bf \implies x = 17$

Measure of parallel sides are

• x = 17cm
• x + 6 = 17 + 6 = 23cm

Therefore, parallel sides of trapezium is 17cm and 23cm.

Answer 2

Answer:

The lengths of parallel sides of trapezium are 17 cm and 23 cm.

Step-by-step-explanation:

We have given that,

Area of trapezium = 180 sq.cm

Height = 9 cm

Let the one parallel side of trapezium be x cm.

From the given condition,

One parallel side of trapezium is longer than other by 6 cm.

∴ Other parallel side = One parallel side + 6

Other parallel side = ( x + 6 ) cm

We know that,

Area of trapezium = ( Sum of parallel sides ) * Height / 2

⇒ 180 = [ x + ( x + 6 ) ] * 9 / 2

⇒ 180 * 2 = ( x + x + 6 ) * 9

⇒ 360 = ( 2x + 6 ) * 9

⇒ 360 = 18x + 54

⇒ 18x = 360 - 54

⇒ 18x = 18 ( 20 - 3 )

⇒ x = 20 - 3

⇒ x = 17

∴ One parallel side = 17 cm

Now,

Other parallel side = ( x + 6 ) cm

⇒ Other parallel side = ( 17 + 6 ) cm

⇒ Other parallel side = 23 cm

∴ The lengths of parallel sides of trapezium are 17 cm and 23 cm.