word problem need help asap

Question

In this diagram, a rope is attached to a small pulley at the apex of an isosceles prism. What is the minimum length of the rope (r) needed to span the sides of the prism, rounded to the nearest whole number?

Answer 1

The diagram should be a side view showing the pulley at the top ("the apex") of the prism.  The two sides of the prism are of equal length ("isosceles prism").  That slant length is the hypotenuse of a triangle with height of the prism and length that is half of the base of the prism.

 

The Pythagorean Theorem is very useful here.  The square of the hypotenuse is the sum of the squares of the legs of a right triangle:     c² = a² + b².   Be sure to use half of the prism base as one leg and the height of the prism as the other leg.  Square those numbers, add the squares, then find the square root of the sum so you can determine the length of one slope.

 

Lastly, realize that the rope has to go up one side and down the other side of the prism.  So, double the length of the hypotenuse (since they are the same length) to get the minimum length of rope that is needed.