Sat math Essentials

15.
21
Both figures contain five angles. Each figure
contains three right angles and an angle
labeled 105 degrees. Therefore, the corre-
sponding angles in each figure whose meas-
ures are not given (angles 
B
and 
G,
respectively) must also be equal, which makes
the two figures similar. The lengths of the
sides of similar figures are in the same ratio.
The length of side 
FJ
is 36 units and the
length of its corresponding side,
AE
, in figure
ABCDE
is 180 units. Therefore, the ratio of
side 
FJ
to side 
AE
is 36:180 or 1:5. The lengths
of sides 
FG
and 
AB
are in the same ratio. If
the length of side 
FG
is 
x
, then:
10
x
5
= 
1
5
, 5
x
=
105,
x
= 21. The length of side 
FG
is 21 units.
16.
4
DeDe runs 5 mph, or 5 miles in 60 minutes.
Use a proportion to find how long it would
take for DeDe to run 2 miles:
6
5
0
= 
2
x
, 5
x
= 120,
x
= 24 minutes. Greg runs 6 mph, or 6 miles
in 60 minutes. Therefore, he runs 2 miles in
a
b
– 
a
a
1
1
a
–
P R A C T I C E T E S T 2
–
2 1 7

---

6
6
0
= 
2
x
, 6
x
= 120,
x
= 20 minutes. It takes
DeDe 24 – 20 = 4 minutes longer to run the
field.
17.
84
If point 
A
is located at (–3,12) and point 
C
is
located at (9,5), that means that either point 
B
or point 
D
has the coordinates (–3,5) and the
other has the coordinates (9,12). The differ-
ence between the different 
x
values is 9 – (–3) =
12 and the difference between the different 
y
values is 12 – 5 = 7. The length of the rectan-
gle is 12 units and the width of the rectangle is
seven units. The area of a rectangle is equal to its
length multiplied by its width, so the area of
ABCD
= (12)(7) = 84 square units.