Question

A rectangle has an area of 20, both sides are integers. What are possible lengths for the sides? Which would give you the largest perimeter?

Answer 1

`\begin{gathered} \text{Area =20} \\ \text{Let' sassume the l and b is the length and the width of the rectangle.} \\ So, \\ l* b=20\Rightarrow b=(20)/(l) \\ \text{Now,perimeter } \\ \text{p}=2(l+b) \\ \text{For largest perimeter, differentiate the above equation} \\ (dP)/(dl)=(d2(l+b))/(dl) \\ (dP)/(dl)=(2d(l+(20)/(l)))/(dl) \\ 0=2-(40)/(l^2) \\ 2=(40)/(l^2) \\ l^2=20 \\ l=4.47\text{unit} \end{gathered}`