<p>I would appreciate it if someone could explain #16 on page 673 of the Collegeboard's "Official SAT Study Guide". Thanks</p>
<p>Draw a line from A to D. Note the vertical angles formed on AD. Call the point of intersection between AD and BC whatever you want...how about point X.</p>
<p>Because of the vertical (and thus, congruent) angles, and the fact that ABX and CDX are similar right triangles, you can use proportions to solve for the length of BX and CX. Once you get these lengths, you can just perform the Pythagorean Theorem for ABX and CDX, add those hypotenuse values up, then subtract that number from 16 + 15 + 4.</p>
<p>Solution...</p>
<p>16/(15 - x) = 4/x
16x = 60 - 4x
20x = 60
x = 3
So, CX = 3 and BX = 12.</p>
<p>ABX's hypotenuse: (16^2 + 12^2)^(1/2) = 20
CDX's hypotenuse: (3^2 + 4^2)^(1/2) = 5
AD length = 25</p>
<p>35 - 25 = 10, (C).</p>
<p>Hopefully I will be able to explain it cleary - Here goes ....</p>
<p>1) First find out how many miles it takes Diane to travel the long way
16 + 15 + 4 = 35</p>
<p>2) Make a point "E" at the intersection of both triangles (making two right triangles) ... point E shoud be a little below the C point</p>
<p>3) Think of common right triangles
(3,4,5) (8,17,24) etc, etc</p>
<p>4) The smaller triangle CDE has a 4 .... thus CE = 3 and DE= 5
5) Since CE=3 , BE= 12 ..... (12 + 3= 15 <-- segment BC)
6) Now you know that BE=12, AB= 16..... AE must equal 20!
7) Add the hypotenuse of both triangles ... 20 +5 = 25
8) 35-25 = 10
C is the answer.... hope you are not still confused</p>