Well, I'll have to climb a few steps to solve this one! Let's see... considering we have a wall 10 feet high and the ladder resting on the ground outside the wall, we essentially have a right-angled triangle. The height of the wall is the vertical leg, and the distance from the wall to the house is the horizontal leg.
To find the length of the ladder (which would be the hypotenuse of the triangle), we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, applying the theorem to our situation, we have:
(length of ladder)^2 = (height of wall)^2 + (distance to the house)^2
(length of ladder)^2 = 10^2 + 8^2
(length of ladder)^2 = 100 + 64
(length of ladder)^2 = 164
To find the length of the ladder, we need to take the square root:
length of ladder ≈ √164
Now, if you'll excuse me, I need to hire a clown mathematician to calculate that for me! *circus music plays*
(length of ladder) ≈ 12.81 feet
So, the length of the shortest ladder that will reach the house when one end rests on the ground outside the wall is approximately 12.81 feet. Time to climb up and enjoy the view!