Question

A farmer has enough money to build only 100 meters of fence. What are the dimensions of the field he can enclose with the maximum area?

A 25m x 25m

B 20m x 30m

C. 15m x 35m

D. 22.5m x 27.5m

Answer 1

Solve using mensuration formulas

$2x+2y=100\\x+y=50\\y=50-x\\area\space= xy\\=X=X(50-x)=50x-x^2\\\frac{dA}{dx}=50-2x$

For maximum area

$\frac{dA}{dx}=0=50-2x\\x=25\\so\\y=50-25=25$

The dimensions of field is 28×25