Question

Find the length of a fence that surrounds a square garden if the length of one side of

the garden is given. Are the length of the fence and the length of one side directly
proportional quintities? Explain.
2 in
Help

Answer 1

Explanation:

the perimeter/circumference of a square is simply 4 times one side length, because all side lengths are the same.

we could also say

side + side + side + side

and that is simply 4×side.

as the perimeter (= length of the fence) is calculated

as 4×side, any change factor of the side length goes 1:1 into the perimeter calculation.

let's say the side length changes by a factor f

side new = side old × f

perimeter old = 4 × side old

perimeter new = 4 × side new = 4 × side old × f

so, if the side length changes by the factor f, then also the perimeter changes by the factor f.