Question

area of house is in the shape of a trapezium with parallel side in the ratio 3 ratio 5 its area is 50 m square that the perpendicular distance between the parallel side is 5 metres.find the length of two parallel side of that open area

Answer 1

Given that
area = 50 m²

Perpendicular distance (height) = 5 m

Ratio of parallel sides = 3 : 5


Let the parallel sides be 3x and 5x

Now we know that the area of a trapezium is

1/2 × (sum of parallel sides) × height = area

Here, putting the values we get

=> 1/2 × (3x + 5x) × 5 = 50

=> 5/2 × (8x) = 50

=> 8x = 50 × 2/5

=> 8x = 20

=> x = 20/8

=> x = 5/2

Now first side = 3x

=> 3 × 5/2

= 15/2 metres

= 7.5 metres

Second side = 5x = 5 × 5/2

= 25/2 metres

= 12.5 metres


Hope it helps dear friend ☺️

Answer 2

Let the parallel sides be 3x and 5x.

Area of trapezium = 1/2*(sum of parallel sides)*height

50 = 1/2*(3x+5x)*5

8x=20

x=2.5 m

Length of parallel sides = 3*2.5 = 7.5 m, 5*2.5 = 12.5 m