Question

Find the measures of parallel sides of a trapezium whose ratio is 4:9, area is 390 2 and
distance between the parallel sides is 15 m.

Answer 1

Answer:

Area of trapezium = a+b/2*h = 390^2m

h = 15m

a = 4x

b = 9x

4x + 9x / 2 * 15 = 390

13x / 2 * 15 = 390

13x * 15 = 390 * 2

13x = 780 / 15

13x = 52

x = 52 / 13

x = 4

Therefore,

side 1 = a = 4x = 4*4 = 16m

side 2 = b = 9x = 4*9 = 36m

Verification:

16+36/2 * 15

52/2 * 15

26 * 15

= 390

Answer 2

Correct Question:-

Find the measures of parallel sides of a trapezium whose ratio is 4:9, area is 390 m² anddistance between the parallel sides is 15 m.

Given:-

• Ratio of parallel sides = 4:9
• Height of trapezium = 15 m
• Area of trapezium = 390 m²

To Find:-

• Parallel sides of trapezium

Solution:-

Put x in the ratio,

• First side = 4x
• Second side = 9x

$\: \: \: \: \: \: \: \: \: \: \: \mathfrak{ \underline{ \green{ Formula \: to \: calculate \: the \: a rea \: of \: trapezium}}}$

$\boxed{ \mathfrak{ \large{ \star \: \: \: \: \: { \red{area = \frac{sum \: of \: parallel \: sides}{2} \times height}}}}}$

According to question,

$\large{ \tt \longmapsto \: \: \: \: \: \: \: \: \frac{4x + 9x}{2} \times 15 = 390}$

$\large{ \tt \longmapsto \: \: \: \: \: \: \: \: 13x \times 15= 390 \times 2}$

$\large{ \tt \longmapsto \: \: \: \: \: \: \: \: 13x = \frac{390 \times 2}{15} }$

$\large{ \tt \longmapsto \: \: \: \: \: \: \: \: 13x = 52}$

$\large{ \tt \longmapsto \: \: \: \: \: \: \: \boxed{ \mathfrak{ \pink{x = 4}}}}$

Now,

• First side = 4x = 16 m
• Second side = 9x = 36 m

Hence,

• The parallel sides of trapezium are 16 m and 36 m