Question

Alberto wants to keep their favorite tree from being uprooted by heavy winds. They plan to tie 3 sections of rope to a band on the trunk of the tree, 5 feet above the ground. They will tie each section of the rope to a stake in the ground 12 feet out from the base of the tree. How much rope will he need altogether?

Answer 1

39 ft

Explanation:

Using the description as a guideline I have drawn out the situation (badly drawn) as seen in the picture below. From the picture, we see that we need to find x which is the length of one of the ropes. Once we have this length we simply multiply it by 3 to find out how much rope we need altogether. Since this is the diagonal of a triangle we can use the Pythagorean theorem to solve for x.

Pythagorean theorem:
`a^(2) +b^(2) = c^(2)` .... which a and b are the two sides while x is the diagonal.

`5^(2) +12^(2) = x^(2)`

`25 + 144 = x^(2)`

`169 = x^(2)` ... now we square root both sides

`13 = x`

Now that we have the length of one of the ropes we simply multiply this by 3 to find the total amount of rope needed.

13 * 3 = 39 ft