SAT Question of the Day August 2nd 2013

A 25-foot ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on concrete 7 feet from the base of the building. If the top of the ladder slips down 4 feet, then the bottom of the ladder will slide out

A.     4 feet

B.     5 feet

C.     6 feet

D.     7 feet

E.     8 feet

One of the hardest SAT questions of the day I’ve seen so far.

It requires knowledge of the pythagorean theorem and for most students, a use of a calculator.

Lets draw a diagram that will help us understand what is going on.

We have a 25 foot ladder (constant length) leaning against a wall. This creates a right triangle with the floor. The base is 7 feet from the wall. Using pythagorean theorem (the sum of the squares of the lengths of a right triangle equals the square of the length of it’s hypotenuse).

c^2=b^2+a^2

Using this theorem we conclude the ladder’s top is 24 feet from the ground.

25^2=7^2+a^2

625=49+a^2

576=a^2

24=a

Now the ladder slips down 4 feet – that means we now have a different right triangle. The length of the ladder did not change (25 feet) but the distance from the top of the ladder to the ground and from the bottom part of the ladder to the wall both do. Now we look for our b

25^2=20^2+b^2

625=400+b^2

225=b^2

15=b

The ladder then slides from it’s initial location, 7 feet from the wall, to a new location 15 feet from the wall. It was displaced 8 feet.

39% out of 151,000 got it right.

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