19. b. Since
ABC is a right triangle, the sum of the
squares of its legs is equal to the square of the
hypotenuse: (
AB )
2
+ 8
2
= 10
2
, (
AB )
2
+ 64 = 100,
(
AB )
2
= 36,
AB = 6 units. The diameter of cir-
cle
O is
2
3
of
AB , or
2
3
(6) = 4 units. The area of a
triangle is equal to
1
2
bh , where
b is the base of the
triangle and
h is the height of the triangle. The
area of
ABC =
1
2
(6)(8) = 24 square units. The
area of a circle is equal to
π
r 2
, where
r is the
radius of the circle. The radius of a circle is
equal to half the diameter of the circle, so the
radius of
O is
1
2
(4) = 2 units. The area of circle
O =
π
(2)
2
= 4
π
. The shaded area is equal to the
area of the triangle minus the area of the circle:
24 – 4
π
square units.
20. c. Let 3
x equal the number of four-person booths
and let 5
x equal the number of two-person
booths. Each four-person booth holds four peo-
ple and each two-person booth holds two peo-
ple. Therefore, (3
x )(4) + (5
x )(2) = 154, 12
x +
10
x = 154, 22
x = 154,
x = 7. There are (7)(3) =
21 four-person booths and (7)(5) = 35 two-
person booths.
Section 2 Answers
