The area of a parallelogram is y cm² 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.

Given:

Area of the first parallelogram = y cm²

Height of the first parallelogram = h cm

Area of the first parallelogram = base x height

⇒ y = base x h

⇒ base of the first parallelogram = $\dfrac{y}{h}$ cm

The base of the second parallelogram = $\Big(\dfrac{y}{h} + x\Big)$ cm

Area of the second parallelogram = base x height

⇒ $2y = \Big(\dfrac{y}{h} + x\Big)$ x height

⇒ height = $\dfrac{2hy}{y + hx}$

Hence, the height of the second parallelogram is $\dfrac{2hy}{y + hx}$.