Find the two parallel sides of a Trapezium whose area is 1.6m² altitude is 10 dm and one of the parallel side is longer than other by 8 dm.
Answers
Hey User!!!
according to the question, the length of one of the paralel side of the trapezium is 8dm longer than the other.
let the shorter parallel side be x.
therefore the longer parallel side = x + 8
altitude of the trapezium is given 10dm and area of the trapezium = 1.6m^2
we know that 1m^2 = 100dm^2
therefore 1.6m^2 = 100 * 1.6 = 160dm^2
the formula for finding the area of trapezium is 1/2*h(b1+b2) where "h" is the altitude of the trapezium and b1 and b2 are the parallel sides of the trapezium.
>> 1/2 * h (b1 + b2) = 160dm^2
>> 1/2 * 10 (x + x + 8) = 160dm^2
>> 5 (2x + 8) = 160dm^2
>> 10x + 40 = 160dm^2
>> 10x = 160 - 40
>> 10x = 120
>> x = 120/10
>> x = 12
hence, parallel sides of the trapezium are :-
>> b1 = x = 12dm
>> b2 = x + 8 = 12 + 8 = 20dm
verification :-
= 1/2 * h ( b1 + b2 )
= 1/2 * 10 ( 12 + 20 )
= 5 * 32
= 160dm^2
hence verified..