Download CHAPTER 3: Applications of Algebra Section 3.3: Geometric Problems

MATH 0960
Section 3.3 Notes
CHAPTER 3: Applications of Algebra
Section 3.3: Geometric Problems
Topics: (not from the book)
A. Solve perimeter problems.
B. Solve angle problems.
C. Solve visual problems.
A. Solve perimeter problems.
 What does a problem look like?
Example: Solve the following geometric problem.
The perimeter of a rectangular fence is 800 ft. Find the dimensions of the
rectangle if the length is one foot more than quadruple the width.
Solution:
( )
width
length
(
)
Dimensions

What do I need to know?
o The perimeter of a closed geometric shape is the total distance around its
outside edges.
o The dimensions of a rectangle are its length and width; dimensions are
usually written as “length by width” or “length x width.”
o The formula for the perimeter of any rectangle is
B. Solve angle problems.
 What does a problem look like?
Examples: Solve the following geometric problems.
1. Angles A and B are complementary angles. Angle B is 3 times larger than
angle A. Find the measures of the angles.
Solution:
angle A (degrees)
angle B (degrees)
Angle
Angle
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MATH 0960
Section 3.3 Notes
2. The largest angle of a triangle is 3 times the smallest. The other angle is 5°
more than the smallest. Find the angles.
Solution:
the smallest angle (degrees)
the largest angle (degrees)
the other angle (degrees)
The smallest angle
The largest angle
The other angle

What do I need to know?
o A degree (denoted by °) is a unit of measure equaling 1/360 of a full
revolution.
Examples:
1.
2.
o An angle is the distance between two rays (line segments) which meet at a
vertex commonly measured in degrees.
o Complementary angles are any two angles whose sum is 90°.
o Supplementary angles are any two angles whose sum is 180°.
o A triangle is a closed geometric shape with 3 sides (and consequently 3
angles); the sum of the interior angles of a triangle is 180°.
o An isosceles triangle is one with two sides of equal length and two equal
angles.
o A quadrilateral is a closed geometric shape with 4 sides (and consequently 4
angles); the sum of the interior angles of a quadrilateral is 360°.
o A parallelogram is a quadrilateral with two pairs of sides with equal lengths
and two pairs of equal angles; in a parallelogram, opposite angles are equal.
o A rhombus is a quadrilateral in which all four sides have equal length and
two pairs of equal angles; in a rhombus, opposite angles are equal.
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MATH 0960
Section 3.3 Notes
C. Solve visual problems.
 What does a problem look like?
Example: Solve the following geometric problem.
A rectangular area is to be fenced in along a straight river bank as illustrated.
The length of the fenced-in area is to be twice the width, and the total amount of
fencing to be used is 210 feet. Find the dimensions of the fenced-in area.
Solution:
width (feet)
length (feet)
Dimensions: 30 ft. by 60 ft.

What do I need to know?
o The perimeter of a closed geometric shape is the total distance around its
outside edges.
o The dimensions of a rectangle are its length and width; dimensions are
usually written as “length by width” or “length x width.”
o In these problems you will usually be given a total length which equals the
sum of all lengths involved.
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