# SAT Math: Geometry

## Triangles

A 15 foot ladder is left leaning against a wall.  The base of the ladder is 12 feet from the wall.  How many feet above the ground does the ladder touch the wall?

A.  8

B.  9

C.  10

D.  11

E.  12

## Knowsys Method

Read the question carefully.  There is no diagram in this problem, but it might help you keep the measurements straight if you draw one.  Start with the ladder.  It is at a diagonal from the ground to the wall.  This must be your hypotenuse.  Remembering that the ground and the wall are perpendicular, draw a right triangle with a hypotenuse of 15.  Then add that the length between the ladder and the wall (the horizontal length) is 12.  You have accounted for all the information provided in the problem.

Identify the bottom line.  What is the length of the last side of the triangle?

Assess your options.  Many students will use the Pythagorean Theorem to solve this problem, but there is a much faster method.  Your Knowsys handbook asks you to memorize the Pythagorean Triplet 3-4-5.  These numbers represent the ratio of the sides of a right triangle.  Notice that if you multiply these numbers by 3, you will get two of the numbers of your right triangle.  Use this method to find the third side of your triangle without wasting time squaring and taking the root of any of the numbers.

Attack the problem.    Start by knowing that the 3-4-5 triangle can be enlarged by multiplying each of the sides by the same number.  Compare it to your triangle.

3-4-5

? -12-15

Notice that if you multiply the original 4 by 3, you get 12.  If you multiply the original 5 by 3, you get 15.  In order to get the missing side, all you need to do is multiply the original 3 by 3.

3 x 3 = 9

Loop back.  You found the length of the missing side, so you are finished.

Note: If you have time after finishing all the other problems, you can check this problem using the Pythagorean Theorem, but there is no need to use it before then.