Question

9. The ratio of the parallel sides of a trapezium is 3:5
and the perpendicular distance between them is
16 cm. If the area of the trapezium is 384 sq. cm, find
the length of each parallel side.

Answer 1

Given:

A trapezium with

• Ratio of sides = 3 : 5
• Perpendicular distance (Height) = 16 cm
• Area = 384 sq. cm

What To Find:

We have to find the sides of the trapezium.

How To Find:

To find the sides of the trapezium of sides, we have to

• Take x as the common multiple in the ratio - 3 : 5 = 3x : 5x
• Use the formula i.e. $\sf{ Area = \dfrac{a + b}{2} \times h}$ where a = 3x and b = 5x.
• Substitute the values and solve.

Solution:

Using the formula,

⇒ $\sf{ Area = \dfrac{a + b}{2} \times h}$

Substitute the values,

⇒ $\sf{ 384 \: sq.cm = \dfrac{3x + 5x}{2} \times 16}$

Add the numerator,

⇒ $\sf{ 384 \: sq.cm = \dfrac{8x}{2} \times 16}$

Cancel 2 and 16,

⇒ 384 sq.cm = 8x × 8

Multiply 8x and 8,

⇒ 384 sq,cm = 64x

Take 64 to LHS,

⇒ $\sf{\dfrac{384}{64} = x}$

Divide 384 by 64,

⇒ 6 = x

Now, substitute the values,

• 3x = 3 × 6 = 18 cm
• 5x = 5 × 6 = 30 cm

∴ Therefore, the sides of the trapezium are 18 cm and 30 cm.