Question

The area of a trapezium is 384 cm square. It's parallel sides are in the ratio 3:5 and the distance between them is 12 cm. Find the length of each parallel side................ Plz answer, u will get 20 points. And plz do on a paper and draw a trapezium and show me the distance, parallel sides, etc..

Answer 1

heya Mate!

as we know the area of the trapezium is -

½ · (sum of parallel sides) · height

So,

We have given :

• Area of trapezium = 384 cm²

• Ratio of the parallel sides = 3:5

• height of the trapezium or the Distance between the two // sides = 12 cm.

Solution :

½ · (3x + 5x) · 12 = 384 cm²

½ · 8x · 12 = 384 cm²

7x = 384 · 2/12

8x = 64

x = 8 cm.

Then the parallel sides would be :

3x = 24 cm.

5x = 40 cm.

Answer 2

* Reference of trapezium is in the attachment.

AnswEr:-

Length of each parallel sides=24cm & 40cm

$\rule{200}{1}$

As the given parallel sides of the trapezium is 3 : 5.

So,Let's take the parallel sides as 3y & 5y.

It is also given that the area of trapezium is 384 cm² and the distance between two parallel sides is 12 cm.

As we know,

$\bf{\dag}\: {\boxed{\sf{Area \: of \: trapezium = \dfrac{1}{2}(Sum \: of \: parallel \: sides)\times Height }}}$

• Putting values:-

$\twoheadrightarrow\sf 384 = \dfrac{1}{2}(3y + 5y)\times 12 \\\\\twoheadrightarrow\sf 384 = \dfrac{12(8y)}{2} \\\\\twoheadrightarrow\sf 96y = 768 \\\\\twoheadrightarrow\sf y = \cancel{\dfrac{768}{96}} \\\\\twoheadrightarrow\large{\underline{\boxed{\sf\blue{y = 8 \: cm }}}}$

$\rule{150}{2}$

◗ One parallel side = 3y = 3(8)= 24 cm

◗ 2nd parallel side = 5y = 5(8) = 40 cm

Therefore,

Two parallel sides of trapezium are 24 cm & 40 cm.