Answer:
z = [tex]\sqrt{10}[/tex]
Step-by-step explanation:
Small triangle:
short leg = 2
long leg = z
Large triangle
short leg = z
long leg = 5
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The triangles are similar therefor
Sshort / Lshort = Slong / Llong
2/z = z/5
multiply both sides by z
2 = [tex]z^{2}[/tex]/5
multiply both sides by 5
10 = [tex]z^{2}[/tex]
Take the square root of both sides
z = [tex]\sqrt{10}[/tex]
