What are the values of x and y?

Question

∆ABC : AB = 17, AD = 15, DC = x, BC = y, BD = 9

Answer 1

To find the values of x and y, we can use the Triangle Side-Splitter Theorem.

The Side-Splitter Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those two sides proportionally. In triangle ABC, since AD is parallel to BC, we have:

AD/DC = DB/BA or 15/x = 9/17

To solve for x, cross-multiply:

15 * 17 = 9 * x
255 = 9x
x = 255/9
x = 28.33

Now that we have the value of x, we can find the value of y (BC) using the proportion:

DB/BA = DC/BC or 9/17 = 28.33/y

To solve for y, cross-multiply:

9 * y = 17 * 28.33
9y = 481.61
y = 481.61/9
y = 53.51

So, the values of x and y are approximately x = 28.33 and y = 53.51.