Confusing SAT Question of the Day from yesterday. Help please?

<p>A -foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on concrete feet from the base of the building. If the top of the ladder slips down feet, then the bottom of the ladder will slide out</p>

<p>(A) 4 feet
(B) 5 feet
(C) 6 feet
(D) 7 feet
(E) 8 feet</p>

<p>This confuses me, even with the Collegeboard's ''Want a hint?'' button! How would YOU solve this? Help?</p>

<p>I agree. It was confusing.</p>

<p>Draw a triangle. The length of the ladder leaning against it is 25. The distance at the bottom between the base of the ladder and the building's wall is 7. The vertical wall's height is unknown, but by using the Pythagorean Theorem, you can do 25^2 - 7^2 = 576. The square root of this is 24.</p>

<p>Now you have the original height of the wall (where it meets the top of the ladder). Then, the top of the ladder drops 4 feet, so 24-4=20. 20 feet represents the new height of the top ladder's meeting place with the vertical wall.</p>

<p>Using the Pythagorean Theorem again to find the new length of the base, 25^2 - 20^2= 225. The square root of this is 15. Now you have the new length of the base is 15. New length - original length = length the ladder slid out, so 15-7=8.</p>

<p>I'm definitely sure there is an easier way to answer this. Math is not my strongest subject :) Hope this helped.</p>

<p>I remember how I became completely bemused when I first saw this (I've seen it before, it was in one of the practice tests)</p>

<p>Well, for starters, you should draw it. You'll notice that it is a 60-90-30 right triangle with 1 unknown side.The ladder is the base,the ground between the ladder and the wall is one of the sides and the wall's length - the other.The right angle, logically, is the space between the wall and the ground . You apply the pythagorean theorem to find the wall length .</p>

<p>7^2(the distance between the ladder and the building) +x^2(the wall on which the ladder is placed) = 25^2(ladder length)</p>

<p>You do the math and find out that the wall distance is 24.</p>

<p>Then you proceed to step 2 - the movement.</p>

<p>You know that the top of the ladder slides down 4 inches, which means that the bottom will also slide down , but you don't know how much, so you name it x. Consequently, if the ladder slides down the wall by 4 feet, the wall's length will be reduced by 4 feet as well.
24-4 = 20.</p>

<p>So, you've got yourself a triangle with 1 unknown side again. The ladder is 25 (as always) , since the ladder has slipped, the distance of the wall is 20 and you need to find the distance between the ladder's bottom and the wall. You set up a pythagorean theorem ,again.</p>

<p>20^2(the wall length + x^2 ( distance between the ladder's bottom and the wall) = 25^2 (the ladder length)</p>

<p>Great! You now know the distance has become 15. Before the ladder slipped it was 7. How longer it had become? 15-7 = 8.</p>

<p>Well, I hope you understood me. But personally I think an actual drawing on paper would be more apt to explain this one.</p>

<p>Ok thank you :)</p>