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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 Page 1 of 3 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. Page 2 of 3 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. Page 3 of 3