Question

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 1

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 = 4*2 = 8cm. (Ans.)

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

Hence, Height and two parallel sides of given trapezium are 6cm , 8 cm and 10cm respectively .