Answer:
Part A: [tex]l = 60[/tex], Part B: [tex]b = \frac{9\sqrt{2}}{2}[/tex]
Step-by-step explanation:
The Pythagorean Theorem determines the length of the hypotenuse of right triangle ([tex]r[/tex]) by means of following formula:
[tex]r^{2} = x^{2}+y^{2}[/tex] (1)
Where [tex]x[/tex], [tex]y[/tex] are respective lengths of each leg.
Now we proceed to solve on each triangle:
Part A: ([tex]r = l[/tex], [tex]x = y = 30\sqrt{2}[/tex])
[tex]l^{2} = (30\sqrt{2})^{2}+(30\sqrt{2})^{2}[/tex]
[tex]l^{2} = 3600[/tex]
[tex]l = 60[/tex]
Part B: ([tex]r = 9[/tex], [tex]x = b[/tex], [tex]y = \frac{9\sqrt{2}}{2}[/tex])
[tex]9^{2} = b^{2}+\left(\frac{9\sqrt{2}}{2} \right)^{2}[/tex]
[tex]81 = b^{2}+\frac{81}{2}[/tex]
[tex]b^{2} = \frac{81}{2}[/tex]
[tex]b = \frac{9\sqrt{2}}{2}[/tex]
