in a trapezium shaped field ,one of the parallel sides is twice the other .if the area of the field is 5670 m2 and the perpendicular distances between the two parallel sides is 84 cm , find the length of the parallel sides.
Answers
Given :
- In a trapezium shaped field ,one of the parallel sides is twice the other .if the area of the field is 5670 m² and the perpendicular distances between the two parallel sides is 84 cm.
To Find :
- The length of the parallel sides = ?
Solution :
- Area of the field = 5670 m² = 56700000 cm²
- Height = 84 cm
Let the one parallel sides be x and other parallel side be 2x.
★ According to Question now :
→ Area of trapezium = ½ × (Sum of parallel sides) × Height
→ 56700000 = ½ × (x + 2x) × 84
→ 56700000 = 3x × 42
→ 56700000 ÷ 42 = 3x
→ 1350000 = 3x
→ x = 1350000 ÷ 3
→ x = 450000 cm
Hence,
- One parallel side = x = 450000 cm
- Another parallel side = 2x = 2(450000) = 900000 cm
Verification :
→ 56700000 = ½ × (x + 2x) × 84
→ 56700000 = ½ × (450000 + 900000)× 84
→ 56700000 = 450000 + 900000 × 42
→ 56700000 = 1350000 × 42
→ 56700000 = 56700000
LHS = RHS
Hence, Verified !
Given:-
- In a Trapezium shaped field one of the parallel side is twice the other.
- Area of the field = 5670m²
- Perpendicular distance between parallel sides = 84cm
Find:-
- Length of parallel sides.
Solution:-
Let, f1st parallel side = ❝a❞ cm
and, 2nd parallel side = ❝2a❞ cm
⟶ Area of the field = 5760m²
⟶ Area of the field = 5760×100×100
⟶ Area of the field = 57600000cm²
Now, using
➟ Area of Trapezium = 1/2(sum of parallel sides) × height
➟ Area of Trapezium = 1/2(a + b) × h
where,
- Area of Trapezium = 57600000cm²
- a = a cm
- b = 2a cm
- h = 84cm
* Substituting these values *
➩ Area of Trapezium = 1/2(a + b)×h
➩ 57600000= 1/2(a + 2a)×84
➩ 57600000 = 1/2(3a)×84
➩ 57600000 = 1/2 × 3a ×84
➩ 57600000 = 1/2 × 252a
➩ 57600000 = 252a/2
➩ 57600000 = 126a
➩ (57600000)/(126) = a
➩ 450000cm = a
_______________________
➝Parallel Sides:
❍ ➊st side = a = 450000cm
❍ ➋nd side = 2a = 2×450000 = 900000cm