Question

The area of a trapezium is 180 cm square and it's height is 9 cm. If one of the parallel sides is longer then the other by 6cm , the length of the longer of the parallel sides is

a. 17 cm
b. 23 cm
c. 18 cm
d. 24 cm


​

Answer 1

Answer:

23cm

Step-by-step explanation:

Area of trapezium= 180cm²

height= 9cm

parallel sides= x cm and x+6 cm.

According to question, we have to find length of longer side

Area of trapezium= 1/2x height(sum of parallel sides)

= 180cm² = 1/2x9(x+x+6)

= 180x2= 9(2x+6)

=360= 18x+54

=360-54= 18x

= 306= 18x

x= 17cm

and x+6= 23cm

Hence the longer side is 23cm.

Answer 2

Given

• Are of the trapezium is 180 cm².
• Height of the trapezium is 9 cm.
• On of the parallel sides is longer then the other by 6cm.

⠀

To find

• Length of the longer of the parallel sides.

⠀

Solution

• Let the shorter side be x.
• Then, the longer side be (x + 6)cm.

⠀

$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{As\: we\: know}}}$

⠀

${\dag}\:{\underline{\boxed{\sf{\purple{Area_{(Trapezium)} = \dfrac{Sum\: of\: parallel\: sides}{2} \times height}}}}}$

⠀

Here,

→ Area = 180

→ Sum of parallel sides = x + (x + 6)

→ Sum of parallel sides = 2x + 6

→ Height = 9

⠀

$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Putting\: the\: values}}}$

⠀

$\tt\longmapsto{180 = \dfrac{2x + 6}{2} \times 9}$

⠀

$\tt\longmapsto{180 = (x + 3) \times 9}$

⠀

$\tt\longmapsto{180 = 9x + 27}$

⠀

$\tt\longmapsto{9x = 180 - 27}$

⠀

$\tt\longmapsto{9x = 153}$

⠀

$\tt\longmapsto{x = \dfrac{153}{9}}$

⠀

$\bf\longmapsto{\underline{\boxed{\orange{x = 17}}}}$

⠀

Hence,

• The longer side = x + 6
• The longer side = 17 + 6 = 23cm

━━━━━━━━━━━━━━━━━━━━━━