Mathematics
Grade 9
15 min
Perimeter - Word problems (Advanced)
Perimeter - Word problems (Advanced)
What you'll learn
- Identify the common difference in an arithmetic sequence, given at least three consecutive terms, with 80% accuracy.
- Solve for a specific term in an arithmetic sequence using the explicit formula, given the first term, common difference, and term number, achieving a score of 70% or higher on a quiz.
- Explain, in writing, how the common difference affects the growth of an arithmetic sequence, using accurate mathematical vocabulary, in at least 2 out of 3 attempts.
- Apply the concept of arithmetic sequences to solve real-world problems involving patterns with constant rates of change, demonstrating understanding by correctly answering 3 out of 4 application problems.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Translate complex verbal descriptions of geometric shapes into algebraic expressions and equations.
Formulate and solve quadratic equations that arise from word problems involving the perimeter and area of rectangles.
Set up and solve perimeter problems where side lengths are represented by polynomial expressions.
Analyze and interpret the solutions of equations in the context of a geometric problem, including rejecting non-viable answers (e.g., negative lengths).
Solve for unknown dimensions of composite figures or problems involving multiple related perimeters.
Determine a shape's perimeter when its dimensions are dependent on the solution to a system of equations.
Ever tried to build a custom rectangular fence when you only have enough material fo...
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Key Concepts & Vocabulary
TermDefinitionExample
PerimeterThe total continuous distance around the exterior of a two-dimensional closed shape.For a rectangle with sides 5 cm and 3 cm, the perimeter is 5 + 3 + 5 + 3 = 16 cm.
Algebraic RepresentationUsing variables (like x) and expressions to represent unknown dimensions of a shape based on verbal descriptions.If 'the length of a rectangle is 5 more than twice its width (w)', the length can be represented as the expression '2w + 5'.
Quadratic EquationAn equation that can be written in the standard form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. These often appear when a problem involves both perimeter and area.A problem might lead to the equation x^2 + 5x - 84 = 0, which can be solved for x to find a dimension.
Polynomial Expres...
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Core Formulas
Perimeter of a Rectangle
P = 2l + 2w \quad \text{or} \quad P = 2(l + w)
Used for any four-sided figure with four right angles. 'l' is the length and 'w' is the width. In advanced problems, 'l' and 'w' will often be algebraic expressions.
Perimeter of a Polygon
P = s_1 + s_2 + s_3 + ... + s_n
The perimeter of any polygon is the sum of the lengths of all its sides. This is used for triangles, pentagons, and other irregular shapes where side lengths might be given as different expressions.
The Quadratic Formula
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
A reliable method to solve any quadratic equation in the form ax^2 + bx + c = 0. This is essential when factoring is not straightforward.
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Sign Up Free to ContinueSample Practice Questions
Easy
A triangle has side lengths represented by the polynomial expressions (x + 7), (3x - 2), and (2x + 3). If the perimeter of the triangle is 44 units, what is the value of x?
A.x = 4
B.x = 5
C.x = 6
D.x = 7
Easy
The verbal description 'the length of a rectangle is 4 meters less than twice its width' is translated into which algebraic expression, where 'w' represents the width?
A.l = 4 - 2w
B.l = 2w - 4
C.l = 2(w - 4)
D.l = w - 4
Easy
A rectangular field has a width of 'x' meters. Its length is 5 meters more than its width. Which equation correctly represents the perimeter, P, of the field?
A.P = 2(x + 5) + 2x
B.P = x(x + 5)
C.P = x + (x + 5)
D.P = 2x(x+5)
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Frequently asked questions
What grade level is "Perimeter - Word problems (Advanced)"?
Perimeter - Word problems (Advanced) is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Perimeter - Word problems (Advanced)?
You'll be able to: Identify the common difference in an arithmetic sequence, given at least three consecutive terms, with 80% accuracy; Solve for a specific term in an arithmetic sequence using the explicit formula, given the first term, common….
Is "Perimeter - Word problems (Advanced)" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Perimeter - Word problems (Advanced)?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.