Answer:
z = 3[tex]\sqrt{13}[/tex]
Step-by-step explanation:
Using the altitude- on- hypotenuse theorem
( leg of large Δ )² = ( part of hypotenuse below it ) × ( whole hypotenuse )
z² = 9 × (9 + 4) = 9 × 13 = 117 ( take square root of both sides )
z = [tex]\sqrt{117}[/tex]
= [tex]\sqrt{9(13)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{13}[/tex]
= 3[tex]\sqrt{13}[/tex]
