Question

The area of a parallelogram is 392m². If the altitude is twice the corresponding base, determine the base and the height.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{base}\mathrm{of}\mathrm{parallelogram}=x\mathrm{m} \\ \mathrm{So},\mathrm{length}\mathrm{of}\mathrm{altitude}=2x\mathrm{m} \\ \mathrm{Now}\mathrm{area}\mathrm{of}\mathrm{parallelogram}=392{\mathrm{m}}^2 \\ \mathrm{so},\mathrm{base}\times \mathrm{altitude}=392 \\ \Rightarrow x\times 2x=392 \\ \Rightarrow 2x^2=392 \\ \Rightarrow x^2=196 \\ \Rightarrow x=14 \\ \mathrm{so},\mathrm{base}=14\mathrm{m} \\ \mathrm{altitude}=28\mathrm{m} \end{gathered}$$