Question

The area of a trapezium is 475 sq. cm. Parallel sides are in the ratio 2:3 and height is 10 cm. The length of the longer side is

Answer 1

Given :

⬤ Area of Trapezium is 475 cm².

⬤ Parallel Sides are in the Ratio 2:3 .

⬤ Height of Trapezium is 10 cm.

To Find :

⬤ Length of Longer Side .

Formula Used :

$\bf[\:{Area \: of \: Trapezium = \dfrac{1}{2} \times{(Sum \: of \: Parallel \: Sides)} \times{h}}\:]$

• h = height

Solution :

Let :

• One Parallel Side be = 2x.
• Second Parallel Side be = 3x .

According to the Formula :-

475 = 1/2 × (Sum of Parallel Sides) × h

475 = 1/2 × (2x + 3x) × 10

475 = (2x + 3x) × 5

475 = 10x + 15x

475 = 25x

475/25 = x

19 = x

Therefore , The Value of x is 19 .

Hence ,

One Parallel Side = 2x

= 2(19)

= 38

Second Parallel Side = 3x

= 3(19)

= 57

Therefore , The two Parallel Sides of Trapezium are 38 cm and 57 cm.

Hence , 57 is the Longer Side of Trapezium .

Check :

475 = 1/2 × (Sum of Parallel Sides) × h

475 = 1/2 × (38 + 57) × 10

475 = (38 + 57) × 5

475 = 95 × 5

475 = 475

Hence Checked .

Answer 2

Solution :

Let :

One Parallel Side be = 2x.

Second Parallel Side be = 3x .

According to the Formula :-

475 = 1/2 × (Sum of Parallel Sides) × h

475 = 1/2 × (2x + 3x) × 10

475 = (2x + 3x) × 5

475 = 10x + 15x

475 = 25x

475/25 = x

19 = x

Therefore , The Value of x is 19 .

Hence ,

One Parallel Side = 2x

= 2(19)

= 38

Second Parallel Side = 3x

= 3(19)

= 57

Therefore , The two Parallel Sides of Trapezium are 38 cm and 57 cm.

Hence , 57 is the Longer Side of Trapezium .

Check :

475 = 1/2 × (Sum of Parallel Sides) × h

475 = 1/2 × (38 + 57) × 10

475 = (38 + 57) × 5

475 = 95 × 5

475 = 475