Question

Find the dimensions of a rectangle with area 2,197 m2 whose perimeter is as small as possible. (if both values are the same number, enter it into both blanks.

Answer 1

Area of a rectangle A = l×w = 2197
l - length
w-width
l×w = 2197
making l the subject
l =
`(2197)/(w)`
The perimeter of rectangle
p = 2(l+w)
= 2(w+
`(2197)/(w)`)
=2w+
`(2(2197))/(w)`
To obtain minimal perimeter

`(dp)/(dw)=0`
2-
`(4394)/(w^(2) )` = 0
multiplying both sides of equation by
`w^(2)`
2
`w^(2)`-4394=0
2
`w^(2)`=4394

`w^(2)`=2197
w = √2197
w1 = 46.87
w2 = 46.87