Question

the length of the parrllel sides of a trapezium are in the ratio of 4:7 if the height of trapezium is 14m and its area is 385sq .m find the length of its parrallel sides​

Answer 1

Given:-

• Ratio of parallel sides of trapezium is 4:7.
• Height of trapezium is 14 m.
• Area of trapezium is 385 m².

To find:-

• Length of parallel sides.

Solution:-

Let the one parallel side be '4x'.

And Other parallel side be '7x'.

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We know that,

Area of trapezium = $\sf \: \frac{a + b}{2} \times h$

In which,

• a and b are parallel sides of trapezium.
• h is height of trapezium

⠀⠀⠀

➢ Height = 14 m.

➢ Area of trapezium = 385 m²

⠀⠀⠀

Put , Area of trapezium , height and parallel sides in formula

$\implies \sf \: 385 = \frac{4x + 7x}{2} \times 14$

$\implies \sf \: 385 = 4x + 7x \times 7$

$\implies \sf \frac{385}{7}= 11x$

$\implies \sf 55 = 11x$

$\implies \sf \frac{55}{11}= x$

$\implies \sf 5 = x$

x = 5

⠀⠀⠀

So,

Parallel sides,

4x = 4 × 5 = 20 m

7x = 7 × 5 = 35 m

⠀⠀⠀

Therefore,

Length of parallel sides are 20 m and 35 m.

Answer 2

Step-by-step explanation:

trapezium formula = A= 1/2(a+b)h

Area of trapezium =385sq.m

parrllel sides of trepezium in ratio=4:7

height of trapezium =14m

then lengths of trapezium=?

= 1/2(a+b)h=A

= 1/2(4x+7x)14=385

= 1/2(11x) 14=385

= 14/2* 11x = 385

= 7*11x= 385

= 77x= 385

= x= 385/77

= x = 5

4x= 4* 5=20

7x= 7* 5=35

parrllel sides of trapezium = 20,35