Sat math Essentials

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P R A C T I C E T E S T 2
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2 1 5

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14.
b.
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 base and height of an isosceles
right triangle are equal in length. Therefore,
1
2
b
2
= 18,
b
2
= 36,
b
= 6. The legs of the triangle are
6 cm. The hypotenuse of an isosceles right tri-
angle is equal to the length of one leg multiplied
by 
2
. The hypotenuse of this triangle is equal
to 6
2
cm.
15.
a.
If
a
= 4,
x
could be less than 
a
. For example,
x
could be 3: 4 < 
3
4
(
3
3)
< 8, 4 < 
4
9
3
< 8, 4 < 4
7
9
< 8.
Although 
x
< 
a
is not true for all values of
x
, it
is true for some values of
x
.
16.
c.
The perimeter of a rectangle is equal to 2
l
+ 2
w
,
where 
l
is the length of the rectangle and 
w
is the
width of the rectangle. If the length is one greater
than three times the width, then set the width
equal to 
x
and set the length equal to 3
x
+ 1:
2(3
x
+ 1) + 2(
x
) = 26
6
x
+ 2 + 2
x
= 26
8
x
= 24
x
= 3
The width of the rectangle is 3 ft and the length
of the rectangle is 10 ft. The area of a rectangle
is equal to 
lw;
(10 ft)(3 ft) = 30 ft
2
.