Question

The lengths of the shorter and longer parallel sides of a trapezium are x cm and y cm respectively. If the area of the trapezium is ($x^2 – y^2$), then the height of the trapezium is
A.x
B.(x+y)
C.y
D.2(x+y)

Answer 1

Hint: We know that ${\rm{Area\, of\, Trapezium = }}\dfrac{1}{2} \times {\rm{sum\, of\, parallel\, side}} \times {\rm{height}}$
 so, from this formula we will find height in terms of x and y.

Complete step-by-step answer:
We know that
${\text{Area of Trapezium = }}\dfrac{1}{2} \times {\text{sum of parallel side}} \times {\text{height}}$

So, In the Question given that area of trapezium is ($x^2-y^2$)
So,
 $({x^2} - {y^2}) = \dfrac{1}{2} \times (x + y) \times height$
So, $height = \dfrac{{2({x^2} - {y^2})}}{{x + y}}$
 $ = \dfrac{{2(x + {y})(x - y)}}{{x + {y}}} = 2(x - y)$
[ ∵ $x^2$ – $y^2$ = (x + y) (x – y) ]
So, the height of trapezium = 2 (x – y)
So, from the above option only the D option is correct.

Note: In this type of question, first write the given/known values and use formula to find unknown values. If three values are known in the area of trapezium, then we can easily find the unknown value.