Answer:
[tex]VW = 50[/tex]
Step-by-step explanation:
Given
The attached triangle
Required
Find VW
To find VW, we make use of the following equivalent ratios.
[tex]YX : XW = ZX : XV[/tex]
Where:
[tex]YX = ZX - ZY = 42 - 28 = 14[/tex]
[tex]XV = XW + VW = 25 + VW[/tex]
So, we have:
[tex]14 : 25 = 42 : 25 + VW[/tex]
Express as fraction
[tex]\frac{14 }{ 25 }= \frac{42 }{ 25 + VW}[/tex]
Divide both sides by 14
[tex]\frac{1}{ 25 }= \frac{3}{ 25 + VW}[/tex]
Cross multiply
[tex](25 + VW) * 1 = 3 * 25[/tex]
[tex]25 + VW = 75[/tex]
Solve for VW
[tex]VW = 75 -25[/tex]
[tex]VW = 50[/tex]
