Spring 2014
LAGUARDIA COMMUNITY COLLEGE
Department of Mathematics, Engineering and Computer Science
MAT096 ELEMENTARY ALGEBRA
Textbook: Beginning Algebra, sixth edition (EDUCO)
LAB # 8
Name: ____________________________________
Date: ____________________
Instructor: _________________________________
Section: __________________
You need to show all work. Indicate the right answer in the answer sheet. Even if you mark the right
answer, but do not show work on this sheet, you will not be given credit for that question:
Tutor problems are the examples for the unsolved problem(s) that follow them.
1. (Tutor) The length of a rectangle is 5 feet more than its width, and the area of this
rectangle is 36 square feet. Find its dimensions.
a) Length = 4 ft; width = 9 ft
b) Length = 9 ft; width = 4 ft
c) Length = -9 ft; width = 4 ft
d) Length = 3 ft; width = 8 ft
Solution: Draw a rectangle and let x be the width. Then the length is x + 5.
x+5
x
x
The area of the rectangle is length times width.
Therefore,
Factor completely the expression on the left:
Apply the zero-factor property:
The width cannot be negative, therefore
.
The correct answer is b).
(
(
)
)(
)
or
or
is the only solution. Then, the length =
2. The width of a rectangular floor is 3 feet less than its length. If the area of the floor is
108 square feet, determine the dimensions of the floor.
a) Length = 12 ft; width = 9 ft
b) Length = 9 ft; width = 12 ft
c) Length = -12 ft; width = -9 ft
d) Length = 9 ft; width = 9 ft
Revised Spring 2014
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Spring 2014
3. (Tutor) A top of the ladder is 14 feet high when leaning against the wall. The ladder is
2 feet away from the wall. How long is the ladder?
(Leave your answer in a simplest radical form.)
Solution: Draw a right triangle as shown below. Let
14
be the length of the ladder.
By the Pythagorean Theorem we have:
√
√
Then
2
√
feet
4. A ladder is 10 feet long and leans against a wall. The foot of the ladder is 5 feet from
the wall. How high is the top of the ladder when it is resting against the wall?
(Leave your answer in a simplest radical form.)
5. (Tutor) Simplify: √
2
2
Solution: Recall that 4 and 49 are perfect squares (4 = 2 and 49 = 7 ). This means that
and √ = . Now we can simplify as follows:
√
√
√
6. Simplify:
√
.
√
7. (Tutor) Simplify: √
Solution: √
√
√
√
√
√
√
√ √
√
Revised Spring 2014
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Spring 2014
8. Simplify: √
√
√
9. (Tutor) Simplify:
√
√
√
√
√
√
√
√
√
√
(Rationalizing the denominator)
√
√
√
√
10. Simplify:
√
11. (Tutor) Multiply and simplify: √ ( √
Solution: √ ( √
√
√ )
√ )
√
√
√
√
√
(Using the distributive property)
√
√
√
√
√
√
12. Multiply and simplify: √ ( √
Revised Spring 2014
√
)
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Spring 2014
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Extra Practice Problems
1. If the legs of the right triangle are 5 cm and 12 cm, find the length of the hypotenuse.
2. A lot has the shape of a right triangle. The difference between the two sides is 2
meters. The hypotenuse is 6 meters longer than the longer side. Find the length of the
shorter side.
3. Simplify: √
4. Simplify:
5. Simplify:
√
√
√
√
6. Simplify: √
7. Simplify:
√
√
√
√
Revised Spring 2014
4
A. Drame