Explanation for Question 15 From the Math (Calc) Section on the 2019 May Sat
So question 15 states in the figure above lines, 2 a F B, E, and C D are parallel points of B 3 and E lie on lines AC at F FD, 4 respectively, if AB equals nine, 5 BC equals 18.5 and F E equals 8.5. 6 What is the length of ed to the nearest 10th? 7 So let's start by filling in the information we know, 8 which is that a, B is equal to nine. 9 Let's fill that in BC is equal to 18.5 that 10 goes here. And that F E is equal to 8.1. 11 So now that we fill this information and I'm just going to write an 12 X as a variable for ed, 13 because that's what we're solving for. So because this smaller shape, 14 a B E F fits inside a C D F. 15 And because I F B E N C D are parallel. 16 That means that these two triangles are similar triangles, 17 which means that the ratio of their sides should be equal to each other. 18 So that means that we can set up a ratio using the length of 19 a B and BC. And that should be the same as the ratio of 20 fi F to D. So let's start by doing that. 21 So the ratio of AB to CB is nine over 22 18.5, and that's going to be equal to the ratio of 23 8.5. 24 Sorry, I miswrote that over X. 25 So 8.5 over X. 26 So then all we have to do to solve is to cross multiply and 27 solve for X. So 18.5 times 8.5 28 equals nine, max that's as cross multiplying, 29 and then we can divide both sides by nine and get X is equal 30 to 18.5 times 8.5 31 over nine. And that equals 17. 32 When you put it into a calculator, 17.472 33 with the two repeating, and this question asks us to round to the nearest 34 10th, nearest 10th, and this is the 10th place. 35 So this becomes our, I'm sorry, this is the 10th place. 36 So this becomes 17.5. 37 Oh, the answer is B.