Question

The area of a parallelogram is $$y\ cm^{2} $$ and its height is $$h\ cm$$. The base of another parallelogram is $$x\ cm$$ more than the base of the first parallelogram and its area is twice the area of the first. Find, in terms of $$y, h$$ and $$x$$, the expression for the height of the second parallelogram.

Answer 1

Correct option is A. $$\displaystyle \frac{2hy}{y+xh}\ cm $$
Let the base of parallelogram with area $$y$$ be $$a\ cm$$
$$y=ah$$
$$=>h=\dfrac{y}{a}$$ $$(i)$$
Let $$h'$$ be the height of the other parallelogram.
Again, area of other parallelogram $$=2y$$ and base of the parallelogram $$=a+x$$
$$2y=(a+x)h'$$
$$=>2y= \left(\cfrac{y}{h}+x\right)h'$$ (from $$(i)$$)
$$=>h=\cfrac{2yh}{y+hx}\ cm$$