Today’s SAT question of the day is a cool math problem about a ladder!  Really, it’s kind of fun. The question:

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 how many feet?

First, we have to make a sketch of the initial ladder setup:

Conveniently, we have one of the SAT’s favorite shapes: a right triangle.  We can use the Pythagorean theorem to find the missing side – that is, the height of the ladder on the wall.

5^2 = a^2 + 7^2

…which solves to 24.

Now we have our second step: the top of the ladder slides down 4 feet.  24 – 4 = 20 feet….

(Un)coincidentally, we have another right triangle to solve.

25^2 = b^2 + 20+2

The base of the ladder is now 15 feet from the wall.

15 – 7 = 8 feet; the base of the ladder has moved 8 feet.

Keys to success for this high-difficulty problem: make sketches to isolate the information that you need to find, work methodically to find each missing piece of information, avoid arithmetic errors (and/or use your calculator for the arithmetic!).