FAN+MEDAL
Jarvis needs to determine the distance across a lake. However, he can't measure this distance directly over the water. So, he set up a situation where he could use the measurements of two similar triangles to find the distance across the lake.

He selects a point X such that XZ is perpendicular to VZ, where V is a point at the other end of the lake. He then picks a point Y on XZ. From point Y, he finds point W on XV such that WY is parallel to VZ.

If XY = 3,420 feet, WY = 1,710 feet, and XZ = 10,260 feet, what is the length of VZ, the distance across the lake?

Question

FAN+MEDAL
Jarvis needs to determine the distance across a lake. However, he can't measure this distance directly over the water. So, he set up a situation where he could use the measurements of two similar triangles to find the distance across the lake.

He selects a point X such that XZ is perpendicular to VZ, where V is a point at the other end of the lake. He then picks a point Y on XZ. From point Y, he finds point W on XV such that WY is parallel to VZ.

If XY = 3,420 feet, WY = 1,710 feet, and XZ = 10,260 feet, what is the length of VZ, the distance across the lake?

queelius · Answer

We have the following equation:

$$\frac{ VZ }{ XZ } = \frac{ WY }{ XY }$$

queelius · Answer

XZ, WY, and XY were given, thus we need only solve for VZ.