Step-by-step explanation:
Let the parallel sides be 2x and 3x respectively.
Area of trapezium =420 square cm
Or 1/2×(sum of parallel sides)×(distance between the parallel sides)=420 square cm
Or 1/2×(2x + 3x)×8=420 square cm
Or 1/2 × 5x × 8=420 square cm
Or 20x = 420 square cm
Or x=21 cm
First side =2x =2×21=42 cm
Second side =3x =3×21 =63 cm
Lets furnish the 6th grade maths.
Formula of Area of Trapezium :- (Sum of parallel sides/2)*(perpendicular distance between parallel sides)
Given in the question:-
Parallel sides = 2x and 3x (common factor is assumed as x)
Area = 420
Perpendicular distance = 8
Now put the value in formula.
420 = [(2x + 3x)/2] * 8
5x = 420/4
x = 105/5
x = 21
Hence, parallel sides of trapezium is 42 (2*21) and 63 (3*21).
Correct me if I’m wrong.
Let the parallel sides of the trapezium be AB and CD.
Let AB be 2x and CD = 3x.
The distance between AB and CD = 8 cm.
So the area of ABCD = (AB + CD)*8/2 = 420 or
(2x +3x) = 420/4 = 105, or
5x = 105, or
x = 21.
So AB = 42 cm and CD = 63 cm.
Check: Area of ABCD = (42+63)*8/2 = 105*8/2 = 420 sq cm. Correct.
So the parallel sides of the trapezium are 42 cm and 63 cm.
