Question 1107399
To solve this problem, we need to use the Pythagorean theorem, which is {{{a^2 + b^2 = c^2}}}.


When one draws the ramp, it is evident that you need to find the length of the hypotenuse, "c" (in the following equations, it is represented by "x").

*[illustration Ramp] 


Step 1: Plug in the numbers

{{{84^2 + 35^2 = x^2}}}


Step 2: Simplify

{{{7056 + 1225 = x^2}}}

{{{8281 = x^2}}}


Step 3: Take the square root of both sides (to get "x" by itself)

{{{sqrt(8281) = sqrt(x^2)}}}

{{{91 = x}}}


Final Answer:

The piece of wood is 91 cm long.


Step 4: To check your work, plug your answer back into the theorem

{{{8281 = 91^2}}}

{{{8281 = 8281}}}