The parallel sides of a trapezium are in the ratio 3: 5. Its height is 16 cm and area is 768 cm? Find the lengths of the parallel sides.
Answers
Step-by-step explanation:
Given :-
The parallel sides of a trapezium are in the ratio 3: 5. Its height is 16 cm and area is 768 cm².
To find :-
Find the lengths of the parallel side ?
Solution :-
Given that
The ratio of the parallel sides of a trapezium = 3:5
Let they be 3X cm and 5X cm
Height of the trapezium = 16 cm
We know that
Area of a trapezium = (1/2)h(a+b) sq.units
Where , a and b are parallel sides
h is the height.
Area of the given trapezium
=> (1/2)×16×(3X+5X) cm²
=> (16/2)×8X
=> 8×8X
=> 64X cm²
According to the given problem
Area of the Trapezium = 768 cm²
=> 64X = 768
=> X = 768/64
=> X = 12 cm
If X = 12 cm then the value of 3X
=> 3(12)
=> 36 cm
If X = 12 cm then the value of 5X
=> 5(12)
=> 60 cm
Therefore, the sides are 36 cm and
60 cm
Answer:-
The parallel sides of the trapezium are
36 cm and 60 cm
Check :-
The parallel sides of the Trapezium are 36 cmand 60 cm
Height = 16 cm
Area of the Trapezium = (1/2)×16(36+60)
=> (16/2)×96
=> 8×96
=> 768 cm²
and their ratio = 36:60
=> 36/60
=> (12×3)/(12×5)
=> 3/5
=> 3:5
Verified the given relations in the given problem.
Used formulae:-
→ Area of a trapezium = (1/2)h(a+b) sq.units
Where , a and b are parallel sides
h is the height.