According to the figure, I can safely assume that the 10 cm line and 15 cm line are parallel.
Thus, there are two similar triangles, one with the 10 cm bottom and 15 cm bottom, where one triangle is larger by a factor of 15/10 = 3/2
We know that the 8 cm line segment and y both join to create the side of the large triangle.
8cm + y = the side of the large triangle
Multiplying 8cm by 3/2 gives us 12, since we know the large triangle is 3/2 times larger than the smaller one.
8 + y = 12
y = 4 cm
Finding x is going to be a bit different. We know that the 6 cm line and x form the side of the larger triangle, which we know is 3/2 times larger than x.
x + 6cm = ?
The side of the larger triangle is 3/2x, thus
x + 6 = 3/2 x
Subtract both sides by x
6 = 1/2 x
Multiply both sides by 2
12 cm = x
Thus, y = 4 and x = 12.
Let me know if you need any clarifications, thanks!
