Question

The length of parallel sides of a trapezium are in the ratio 2:3. The distance between the parallel sides and its area are 12 m and 300 m² respectively, then the length of parallel sides are .............................

Answer 1

Answer:

Step-by-step explanation:

Let the proportional constant for sides be x

Then the length of parallel sides will be 3x and 2x meter respectively

Now

Area of trapezium =1/2×sum of parallel

                                sides×height

300=1/2×(3x+2x)×12

300=1/2×5x×12

300=30x

x=10

Hence the length of parallel sides will be

3x=3×10=30m and

2x=2×10=20m.

Answer 2

Answer:

The parallel sides are 20 m and 30 m.

Step-by-step explanation:

Given :

Ratio of parallel sides = 2 : 3

Distance between the parallel sides = 12 m

The area = 300 m²

To find :

The length of parallel sides

Solution :

Let the parallel sides be -

• One as 2y
• Another as 3y

$\rule{300}{1.5}$

★ Area of Trapezium = 1/2 × (Sum of parallel sides) × Height

⇒ 300 = 1/2 × (2y + 3y) × 12

⇒ 300 = 1/2 × 5y × 12

⇒ 300 = 5y × 6

⇒ 5y = 300/6

⇒ 5y = 50

⇒ y = 50/5

⇒ y = 10

$\rule{300}{1.5}$

★ First parallel side -

⇒ 2(y)

⇒ 2 × 10

⇒ 20 m

$\rule{300}{1.5}$

★ Second parallel side -

⇒ 3(y)

⇒ 3 × 10

⇒ 30 m

Therefore, the parallel sides are 20 m and 30 m.