PQRS is a parallelogram. QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm. The value of QN, if PS = 8 cm is _________.

PQRS is a parallelogram. 

QM is the height from Q to SR and QN is the height from Q to PS. 

If SR = 12 cm and QM = 7.6 cm. 

PS = 8 cm

Area of parallelogram = base × height 

Area of parallelogram PQRS = $\mathrm{SR}\times \mathrm{QM}$

Area of parallelogram PQRS = $12\times 7.6$

The area of PQRS = $91.2 {\mathrm{cm}}^2$.

Now, area from other side, with PS as base and QN as height

Area of parallelogram PQRS = $\mathrm{PS}\times \mathrm{QN}$

$\Rightarrow 91.2=8\times \mathrm{h}$

$\Rightarrow \mathrm{h}=\frac{91.2}{8}$

$\Rightarrow \mathrm{h}=11.4 \mathrm{cm}$

Therefore, the value of QN is 11.4 cm.