the height and two parallel sides of a trapezium are in the ratio 3:4:

1.	the height and two parallel sides of a trapezium are in the ratio 3:4:5.Find their lenghts if the area of the trapezium is 54 cm^2
Answer» Given :- The height and two parallel sides of a trapezium are in the ratio 3:4:5. The area of the trapezium is 54 cm^2 . To Find :- Lengths of Height and two parallel sides ? Solution :- Let us ASSUME that, height of trapezium is 3x cm and parallel sides are 4x cm and 5x cm. we know that , → Area of Trapezium = (1/2) * (Sum of parallel sides) * Height . Putting all values and given area we get, → (1/2) * (4x + 5x) * 3x = 54 → 9x * 3x = 54 * 2 → 27x² = 54 * 2 dividing both sides by 27, → x² = 2 * 2 → x² = 2² square - root both sides now, → x = 2 . THEREFORE, → Height of Trapezium = 3x = 3 * 2 = 6cm. (Ans.) → Length of SMALLER parallel SIDE = 4x = 42 = 8cm. (Ans.) → Length of LARGER parallel side = 5x = 52 = 10cm. (Ans.) Hence, Height and two parallel sides of given trapezium are 6cm , 8 cm and 10cm respectively .

the height and two parallel sides of a trapezium are in the ratio 3:4:5.Find their lenghts if the area of the trapezium is 54 cm^2

Answer»

Given :-

To Find :-

Solution :-

Let us ASSUME that, height of trapezium is 3x cm and parallel sides are 4x cm and 5x cm.

we know that ,

→ Area of Trapezium = (1/2) * (Sum of parallel sides) * Height .

Putting all values and given area we get,

→ (1/2) * (4x + 5x) * 3x = 54

→ 9x * 3x = 54 * 2

→ 27x² = 54 * 2

dividing both sides by 27,

→ x² = 2 * 2

→ x² = 2²

square - root both sides now,

→ x = 2 .

→ Height of Trapezium = 3x = 3 * 2 = 6cm. (Ans.)

→ Length of SMALLER parallel SIDE = 4x = 4*2 = 8cm. (Ans.)

→ Length of LARGER parallel side = 5x = 5*2 = 10cm. (Ans.)