Question

Find the dimensions of a rectangle with area 343 m2 whose perimeter is as small as possible.

Answer 1

first take the square root of 343 to find the side length

then multiply that by 4

Answer 2

Courtesy of @MikeyMaximum

xy = 343
y = 343/x
P(x) = Perimeter = 2x+2y
P(x) = 2x + 686x^-1
dP/dx = 2 - 686/x^2 = 0 for maximum or minimum

2x^2 - 686 = 0

x = √ (343) = 7√7

y = 7√7 also

Those are the dimensions.

Concept from @Allan

The minimum perimeter for a rectangle of any given area is a square whose side measure would be the square root of the area.

Answer 3

@hpacheco518