Question

the area of trapezium is 384 cm square its parallel side are the ratio 3:5 and the distance between them is 12 cm find the length of each parallel side ​

Answer 1

Explanation:

Given:

Area of trapezium=384 square cm

Ratio of parallel sides=b_1:b_2=3:5b

1

:b

2

=3:5

Distance between parallel sides=h=12 cm

To find:

Smaller of the parallel sides

Solution:

Let b_1=3x,b_2=5xb

1

=3x,b

2

=5x

Area of trapezium=\frac{1}{2}(b_1+b_2)\times h

2

1

(b

1

+b

2

)×h

Using the formula

384=\frac{1}{2}(3x+5x)\times 12384=

2

1

(3x+5x)×12

384=6(8x)384=6(8x)

x=\frac{384}{6\times 8}=8 cmx=

6×8

384

=8cm

Substitute the value of x

Smaller side=b_1=3\times 8=24 cmb

1

=3×8=24cm

Hence, smaller of the parallel side=24 cm

Answer 2

Answer :

The length of two parallel sides are 24cm and 40cm.

Step-by-step explanation :

To Find,

• The length of each parallel side.

Solution,

Given that,

• The area of trapezium = 384 cm²
• The parallel sides are on ratio of 3 : 5
• The distance between them is 12 cm

Let us assume the ratio sides be 3x and 5x,

As we know that,

★ 1/2 × ( sum of sides ) × distance = Area of trapezium ★

Therefore,

➛ 1/2 × ( 3x + 5x ) × 12 = 384

➛ 1/2 × 8x × 12 = 384

➛ 1 × 8x × 6 = 384

➛ 48x = 384

➛ x = 384 / 48

➛ x = 8

Hence, the value of x is 8.

The length of the parallel sides are,

• The length of the side which we assumed as 3x

➛ 3x

➛ 3 × 8

➛ 24cm ★

• The length of the parallel side which we assumed as 5x

➛ 5x

➛ 5 × 8

➛ 40cm ★

Therefore, the length of the two parallel sides are 24cm and 40 cm.