If a 10 foot ladder is placed against a building so that the distance from the bottom to the building is 2 feet less than the distance from the top of the ladder to the ground. What is the distance from the bottom of the ladder to the building?
Thank you
2007-06-05 08:26:57 · 3 answers · asked by CHRISTOPHER R 1 in Science & Mathematics ➔ Mathematics
6 feet
the 3 sides are 10, x, x-2. that looks like a 3-4-5 right triangle to me.
2007-06-05 08:31:39 · answer #1 · answered by John S 6 · 0⤊ 0⤋
Visualize this as a right triangle. The hypotenuse is the latter, which is 10'. The bottom side is the one you want to solve for: let's call that x. Then the building part (the side) is 2 feet longer, so that's x+2.
From the pythagorean theorem, we know that
x^2 + (x+2)^2 = 10^2
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x + 4 = 100
2x^2 + 4x - 96 = 0
Now you can solve that using the quadratic formula, which will give you two solutions: x = 6, or x = -8. Obviously the bottom side isn't a negative distance, so x = 6.
Therefore the answer to the question is 6.
It's easy to confirm that 6^2 + 8^2 = 10^2.
2007-06-05 15:40:13 · answer #2 · answered by Tamara K 2 · 0⤊ 0⤋
Draw a picture. Dont you smell a 6/8/10 right triangle lurking around?
2007-06-05 15:31:32 · answer #3 · answered by cattbarf 7 · 0⤊ 0⤋