Explanation for Question 15 From the Math (No Calc) Section on the 2017 May Sat
Progression 15. We're going to be talking a little bit about similar triangles and 2 ratios. So the question reads in the figure above BC 3 equals five and the length of the line segment a D 4 is half of the length of the line segment CD. 5 So we know that if AB is X, 6 DC is two X or CD is two X because AVS 7 half, they want to know what is the length of line segment D E. 8 So for some of the triangles, we have a rule that says that the 9 sides are like, if we have this and this, 10 the sides aren't necessarily the same, of course, 11 but they are on a certain proportion. 12 So if this is X and this is three X, 13 this side is also going to be one-third of the side. 14 And the sales are going to be one third of this side. So they 15 are by the same proportions. 16 Now, if X and two X makeup, 17 AC, we know that AC this big line right here is three 18 X. So if we're looking at triangle, 19 H E D K E D and 20 triangle, ABC triangle, 21 a B, C, 22 we know that triangle AEZ the proportion 23 to triangle ABC, or the ratio would be 1, 2, 3, 24 because we're not comparing to the DC. We're comparing a D to 25 a C done in a different color 26 to AC. And if Ady is 27 X, a C is three X, the bigger triangle is three times bigger 28 than the smaller triangle. So if BC is 29 five and we know that five needs to be three times bigger than ed, 30 we know that Eddie is five over a three or 31 C.