The area of a parallelogram is p cm² and its height is q cm. A second parallelogram has equal area but its base is r cm more than that of the first. Obtain an expression in terms of p, q and r for the height h of the second parallelogram.

By formula,

Area of a parallelogram = base × height ……..(1)

Substituting values of 1st || gm in above equation,

⇒ p = base × q

⇒ base = $\dfrac{p}{q}$ cm.

Given,

Base of 2nd || gm is r cm more than the base of 1st || gm.

∴ Base of 2nd || gm = $\Big(\dfrac{p}{q} + r\Big)$ cm.

Given,

Height of second parallelogram = h cm

Substituting the values of 2nd || gm in equation 1,

$\Rightarrow p = \Big(\dfrac{p}{q} + r\Big) \times h \\[1em] \Rightarrow p = \Big(\dfrac{p + qr}{q}\Big) \times h \\[1em] \Rightarrow h = \Big(\dfrac{pq}{p + qr}\Big).$

Hence, h = $\Big(\dfrac{pq}{p + qr}\Big)$ cm.