ANSWER :
The value of w is w = 9/4
EXPLANATION :
From the problem, we have the equation :
[tex]2\sqrt{w+4}=5[/tex]Divide both sides by 2
[tex]\sqrt{w+4}=\frac{5}{2}[/tex]Take the squares of both sides :
[tex]w+4=\frac{25}{4}[/tex]Subtract 4 from both sides :
[tex]\begin{gathered} w+4-4=\frac{25}{4}-4 \\ w=\frac{9}{4} \end{gathered}[/tex]