In `Delta YVW` in Figure, `bar(VX)` is the altitude to side `bar(YW)`, and `bar(ZW)` is the altitude to side `bar(YV)`. If `bar(VX)=3, bar(YV)=4`, and `bar(ZW)=5`, what is the length of side `bar(YW)` ?

Options

A. `4.157`
B. `5.303`
C. `6.667`
D. `6.928`

Answer

C

Explanation

Put the given lengths into the figure :

One - half the product of `bar(YW)` and `bar(VX)` is the same as one-half the product of `bar(YV)` and `bar(ZW)` . Or, ignoring the one - half, you can simply say that the products are equal.
`(1)/(2)(bar(YW))(bar(VX))=(1)/(2)(bar(YV))(bar(ZW))`
`(bar(YW))(bar(VX))=(bar(YV))(bar(ZW))`
`(bar(YW))(3)=(4)(5)`
`(bar(YW))=(20)/(3)~~6.667`