Question

Line segment YV of rectangle YVWX measures 24 units.

Answer 1

Answer: 8√3

Step-by-step explanation:

ΔXVW is a 30°-60°-90° triangle. This special triangle has corresponding sides of lengths: b - b√3 - 2b.  So,

VW = b

XW = b√3

XV = 2b

Since, YV = 24, then XW = 24 and we stated above that XW = b√3. So,

24 = b√3

$\frac{24}{\sqrt{3}} = \frac{b\sqrt{3}}{\sqrt{3}}$

$\frac{24}{\sqrt{3}}$ = b

$\frac{24}{\sqrt{3}}(\frac{\sqrt{3}}{\sqrt{3}})$ = b

$\frac{24\sqrt{3}}{3}$ = b

8√3 = b

We are looking for side YX which is congruent (equal) to VW and we stated above that VW = b, So, VW = 8√3