Answer:
x = 15/2
Step-by-step explanation:
the smaller triangle missing side by using pythagorean theorem
a^2 + b^2 = c^2
4^2 + b^2 = 5^2
b^2 = 25-16=9
b=3 the missing leg for the small triangle;
now use proportionality by saying [tex]\frac{4}{6}[/tex] = [tex]\frac{3}{y}[/tex]; where y is the one leg in the larger triangle
y = 6*3/4 = 9/2
use pythogorean theorem again
a^2 + b^2 = x^2
6^2 + (9/2)^2 = x^2
36 + 81/4 = x^2
144/4 + 81/4 = x^2
225/4 = x^2
x = 15/2
