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:
Today’s ACT question of the day is a repeat of the question we just saw on January 22 about applying the Pythagorean theorem and simplifying radical expressions.
Instead of going over it again, let’s take a moment to remember at least one Pythagorean triplet (3, 4, 5 – a great time save on test day if you know how to apply it).
And, for practice, simplifying another radical expression:
√108 = √(9 * 12 ) = (9 * 4 * 3) = 3√(4 * 3) = 6√3
Check:
6^2 = 36
36 * 3 = 108
No wonder Pythagoras tried to hide in a cave – too much neon in this theorem
Today’s ACT question of the day is asking: do you know the Pythagorean theorem, and can you simplify a radical expression?
If you do and can, this is a 20-second question. If you don’t, you should the Pythagorean theorem now: a^2 + b^2 = c^2. That is, the square of the length of each side (or “leg”) of a right triangle is equal to the square of the length of the hypotenuse. This theorem makes an appearance dozens of times in various ways throughout your test, so keep it with you.
Now that we’ve got that out of the way, let’s apply it! Continue reading