Victory for the ACT Student Text 15e

462 • C AMBRIDGE P RACTICE T EST R EINFORCEMENT

If the perimeter is 12, then each side of the ‹• –Š‡ Š‡‹‰Š–Ǥ ‘ǡ †”ƒ™ ƒ ϐ‹‰—”‡ǣ

44. (G) (p. 388) Mathematics/Geometry/Triangles/Properties of Triangles .

triangle is

4 . The area of a triangle is bh 2 , where b

is the base and h

12

3

Use the Pythagorean theorem to solve for h : 2 4 + = 2 2 2

12 2 = − =

h

16 4

=

=

h

Therefore:

!

2 (length is positive)

12 3

sh 2

Area

triangle

4 ^ h Alternatively, if you remember the formula for the area of an equilateral triangle, you can use that: s 3 2 2 4 2 3 3

Area

equilateral triangle

4

2

4 3

4

16 3

4

4

3

Let 8 x

equal one angle and x

equal the other angle. Since

45. (A) (p. 389) Mathematics/Geometry/Lines and Angles . …‘’Ž‡‡–ƒ”› ƒ‰Ž‡• ƒ†† –‘ ͻͲιǡ ™‡ Šƒ˜‡ǣ x x 8 90 ° + =

x = x 9 90° = 10 °

46. (H) (p. 389) Mathematics/Statistics and Probability/Probability . A square has four right angles; a rectangle has four right angles; a trapezoid does not have four right angles; a circle has no angles. Thus, the probability of four right angles is: # 2 1 of successes

4

2

of possibilities

#