Question

If the area of trapezium is 385cm, It's parallel sides are in ratio 3:4 and perpendicular distance between them is 11cm. Find the length of it's parallel sides.​

Answer 1

now the longer side will be 4x and smaller will be 3x

Answer 2

Answer:

The parallel sides of the Trapezium are 30 cm and 40 cm.

Step-by-step explanation:

Given :

Area = 385 cm

Ratio of sides = 3:4

Perpendicular distance = 11 cm

To find :

The length of its parallel sides

Solution :

Let the parallel sides be -

• One as 3y
• Other as 4y

$\boxed{\sf{Area = \frac{1}{2} \times Sum\: of\:Parallel\:sides \times Height}}$

$\sf{\implies} \: \dfrac{1}{2} \times (3y + 4y) \times 11 = 385 \\ \\ \sf{\implies} \: \dfrac{1}{2} \times 7y \times 11 = 385 \\ \\ \sf{\implies} \: 77y = 770 \\ \\ \sf{\implies} \: y = \dfrac{770}{77} \\ \\ \sf{\implies} \: y = 10$

$\rule{300}{1.5}$

★ Value of 3y

$\sf{\implies} \: 3 \times 10 \\ \\ \sf{\implies} \: 30$

One parallel side = 30 cm

$\rule{300}{1.5}$

★ Value of 4y

$\sf{\implies} \: 4 \times 10 \\ \\ \sf{\implies} \: 40$

Second parallel side = 40 cm

$\therefore$ The parallel sides of the Trapezium are 30 cm and 40 cm.