The lengths of the parallel sides of a trapezium are x cm and y cm and the area of the trapezium is $\frac{1}{2}$(x2 - y2) cm2. What is the distance between the parallel sides (in cm) ?
Answer & explanation
Correct answer: option 1
The area of the trapezium = $\frac{1}{2}$(x2 - y2)
If the lengths of the parallel sides of a trapezium are x cm and y cm and its height is h cm then, the area of the trapezium = $\frac{1}{2}$(x + y)h
The area of the trapezium = $\frac{1}{2}$(x2 - y2) = $\frac{1}{2}$(x - y)(x + y)
$\frac{1}{2}$(x + y)h = $\frac{1}{2}$(x - y)(x + y)
On comparing both of these equations given above,
h = (x - y)