Asquare garden has a diagonal of 34 ft. colton wants to put a fence around the entire garden. how much fencing will he need? round to the nearest foot.

Let s be the length of a side. 

By the Pythagorean Theorem (or knowledge of 45-45-90 triangles) we can find the length of a side from the hypotenuse. 
s² + s² = 34² 
2s² = 34² 
2s² = 1156 
s² = 578 

s = √578 
s ≈ 24.04 

There are 4 sides to the square: 
P = 4s 
P ≈ 96.16 

 
About 96 feet

Ok
pythagorean theorem
a and b are legs, c is hypotonuse (diagonal in this problem)
in square, legs are equal
a=b

a^2+b^2=c^2

diagonal is 34
a=b
a^2+a^2=34^2
2a^2=1156
divide both sides by 2
a^2=578
a=17√2

perimiter is 4 time 1 side for square
p=4 times 17√2
P=68√17 feet

aprox 96.1665 feet

The first option would be correct if it were one half and not one