Question

Equation IQ include many puzzles to advance in the game. 1 puzzle involves a pair of similar triangles. Players must use the clues to find missing side lengths, two triangles are given.

Answer 1

Since the two triangles in the given are similar triangles, we now know that they both have the same angle, but scaled, meaning they have different side lengths.

Base on the given, XA = 15, while XZ = 27

We can now assume that if XA : XZ, BA : YZ

We can rewite this as:

`(XA)/(XZ)=(BA)/(YZ)`

Now, plugging in the values of XA, XZ, and BA, we can now solve for YZ.

`(XA)/(XZ)=(BA)/(YZ)`
`(15)/(27)=(20)/(YZ)`
`15YZ=20(27)`
`YZ=(20(27))/(15)`
`YZ=36`

We now see that the length of YZ is 36 inches.

Next, to solve for XY, we will use the same method, but this time we will be using XB instead of BA.

`(XA)/(XZ)=(XB)/(XY)`

`(15)/(27)=(10)/(XY)`
`15XY=10(27)`
`XY=(10(27))/(15)`
`XY=18`

Therefore, XY is 18 inches long.