Answer: 25 meters.
Step-by-step explanation:
The missing figure is attached.
Draw a Right triangle as the one shown in the second picture, where "a" is the smallest length of rope (in meters) that Ryan could buy, which would stretch from one tree to the other tree.
You need to use the Pythagoream Theorem:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse and "b" are "c" are the legs of the Right triangle.
In this case you can identify that:
[tex]b=25-10=15\\\\c=20[/tex]
Knowing those values, you can susbtitute into [tex]a^2=b^2+c^2[/tex] and then solve for "a" in order to find its value.
You get:
[tex]a^2=15^2+20^2\\\\a=\sqrt{15^2+20^2}\\\\a=25[/tex]
