Question

The area of the trapezium is 784 m². The sum of the parallel sides is equal to twice the value of the height of the trapezium if one of the parallel sides is thrice as another. find the length of the parallel sides. 
1. 14 m and 42 m
2. 12 m and 36 m
3. 16 m and 48 m
4. 10 m and 40 m

Answer 1

Correct Answer - Option 1 : 14 m and 42 m

Given:

The area of the trapezium = 784 m2 

Sum of the parallel sides = 2 × h

Formula Used :

Area of trapezium = 1/2 × (a + b) × h

a & b are parallel sides of the trapezium 

h = perpendicular distance between the parallel sides 

Calculation:

Substituting the values in the formula 

784 = 1/2 × (2h) × h

h = 28 m

the sum of the parallel sides = 2 × 28 ⇒ 56 m

According to the question

let us take the shorter side of the parallel side to be x m

then longer side = 3 × x m

sum of the parallel sides = x + 3x ⇒ 4x

4x = 56 

⇒ shorter side x = 14 m

⇒ longer side 3x = 42 m

∴ The length of the parallel sides is 14 m and 32 m