The two parallel sides and the distance between them are in the ratio 3 : 4 : 2. If the area of the trapezium is 175 cm², find its height.

Given:

The two parallel sides and the distance between them are in the ratio 3 : 4 : 2.

The area of the trapezium is 175 cm².

So, the two parallel sides of the trapezium are 3a and 4a.

Distance between them is 2a.

As we know, the area of a trapezium = $\dfrac{1}{2}$ x (sum of parallel side) x height

⇒ $\dfrac{1}{2}$ x (3a + 4a) x 2a = 175

⇒ $\dfrac{1}{2}$ x 7a x 2a = 175

⇒ $\dfrac{1}{2}$ x 14a² = 175

⇒ 7a² = 175

⇒ a² = $\dfrac{175}{7}$

⇒ a² = 25

⇒ a = $\sqrt{25}$

⇒ a = 5

So, height of the trapezium = 2a

= 2 x 5 cm

= 10 cm

Hence, the height of the trapezium is 10 cm.