The perimeter of a rectangle is 40 cm. Find the dimensions of the rectangle if its area is maximum.

Explanation

Let l and b are the sides of rectangle.
` :. 2(l+b) = 40 `
`rArr l+b = 20` …(1)
If the area of rectangle is A, then
`A= l*b`
`l(20-l)` [From eq. (1)]
`=20 l - l^(2)`
`rArr (dA)/(dl) = 20 - 2l`
For maxima/minima
`(dA)/(dl) = 0`
` rArr 20 - 2l=0`
` rArr l = 10 cm`
And `(d^(2)A)/(dl^(2)) = - 2 lt 0`
`:." At " l = 10 cm`, is maximum.
Therefore, for maximum area, the sides of rectangle are 10 cm and 10 cm.