how much wire is needed

Question

a tree needed to be Staked with three wires each wire is attached to the trunk three feet above the ground a then anchored to the ground 4 feet from the of the tree how much wire is needed for 6 trees

Answer 1

using the Pythagorean Theorem...

the length of wire is the hypotenuse of the right triangle whose legs are 3 feet and 4 feet

let x=length of the wire

3²+4²=x²

9+16=x²

25=x² (if you are familiar, this is a 3-4-5 right triangle)

take the square root of both sides

x=5 feet for the length of one wire

there are 3 wires per tree

3*5=15 feet of wire per tree

there are 6 trees

6*15=90 feet of wire is needed altogether

 

Answer 2

Here a right triangle is formed with 3 ft on the  tree (height, a),  base = 4ft. and  a piece of wire as hypotenuse(c).

 

So , by Pythagorean theorem, b^2 + a^2 = c^2 or 3 ^2 + 4 ^2 = 9 + 16 = 25 = c^2.

 

length of a piece of wire = square root of 25 ft = 5 ft.

 

For one tree you need 3 pieces of wire, combined length of 3 pieces = 3 * 15 = 15ft

 

For 6 trees you need  6 * 15 ft = 90ft. Ans.