Question

Question 16

What are the values of a and b?
10
O
O
O
O
a
a
8
||
||
||
b
9
ain
2
♡
16
-
3
15
2
ain
||
, b
||
b=
||
||
15
―
2
15
▬▬▬▬▬▬▬▬▬
2
9
2
13
2
3.33 pts

Answer 1

Answer:
`a=(9)/(2), b=(15)/(2)`

Explanation:

By the geometric mean theorem,

`√(8a)=6\\\\8a=36\\\\a=(36)/(8)=(9)/(2)`

Using the Pythagorean theorem to solve for b,

`6^(2)+\left((9)/(2) \right)^(2)=b^(2)\\\\36+(81)/(4)=b^(2)\\\\(225)/(4)=b^2\\\\b=(15)/(2)`