Question

The ratio of the length of parallel sides of a trapezium is 2:3 . The distance between them is 16 cm . If the area of the trapezium is 320 sq. cm , find the lengths of the parallel sides ?​

Answer 1

Given :-

• The ratio of the length of parallel sides of a trapezium is 2:3 . The distance between them is 16 cm . If the area of the trapezium is 320 sq. cm.

To find :-

• Length of parallel sides.

Solution :-

Let the parallel sides be 2x and 3x

• Area of trapezium = 320
• Distance between parallel sides = 16cm

As we know that

→ Area of trapezium = ½ × (a + b) × h

Where " (a + b) " sum of parallel sides and " h " is distance between parallel sides.

Now according to question

→ Area of trapezium = 320

→ ½ × (a + b) × h = 320

→ ½ × (2x + 3x) × 16 = 320

→ ½ × 5x × 16 = 320

→ 5x × 8 = 320

→ 40x = 320

→ x = 320/40

→ x = 8

Hence,

• x = 8

Therefore,

• Parallel sides of trapezium

First parallel side = 2x = 16cm

Second parallel side = 3x = 24cm

Answer 2

Answer :-

• 16cm and 24cm.

Given :-

• The ratio of the length of parallel sides of a trapezium is 2:3 . The distance between them is 16 cm and the area of the trapezium is 320cm².

To Find :-

• Length of the parallel sides.

Solution :-

Here,

• Length of parallel sides of a trapezium is 2 : 3 .
• The distance between them is 16cm.
• The area of the trapezium is 320cm².

Put x in the ratio

Then sides will be

• 2x
• 3x

As we know that

Area of a trapezium is

1/2 (sum of parallel sides) × distance between them

According to question :-

320 = 1/2 (2x + 3x) × 16

→ 320 = 1/2 (5x) × 16

→ 320 = 8 × 5x

→ 320 = 40x

→ 320/40 = x

→ x = 8

Put the value of x in the ratio

• 2x = 2 × 8 = 16cm
• 3x = 3 × 8 = 24cm

Hence, the length of the parallel sides are 16cm and 24cm respectively.