Question

There is a rectangular piece of land. its length is 3 more than its breadth. If the length is decreased by 5 units and breadth is decreased by 4 units , the area of the garden will be 800 unit². Frame a quadratic equation to represent this situation and solve the equation by factorization method to find length and breadth. If you had a land like this, how would you use it ? Explain.

Answer 1

Hi,
$$\begin{gathered} \mathrm{Let}\mathrm{breadth}=\mathrm{x} \\ \mathrm{So}\mathrm{length}=\mathrm{x}+3 \\ \mathrm{New}\mathrm{length}=\mathrm{x}+3-5=\mathrm{x}-2 \\ \mathrm{new}\mathrm{breadth}=\mathrm{x}-4 \\ \mathrm{Now}\mathrm{according}\mathrm{to}\mathrm{the}\mathrm{question}, \\ \mathrm{x}\left(\mathrm{x}+3\right)-\left(\mathrm{x}-2\right)\left(\mathrm{x}-4\right)=800 \\ {\mathrm{x}}^2+3\mathrm{x}-\left({\mathrm{x}}^2-6\mathrm{x}+8\right)=800 \\ 9\mathrm{x}-8=800 \\ 9\mathrm{x}=808 \\ \mathrm{x}=\frac{808}{9}=89.78\mathrm{unit} \\ \mathrm{So}\mathrm{length}=\mathrm{x}+3=92.78\mathrm{unit} \end{gathered}$$
Regards