Math Problem Statement
Solution
Let's go through the questions in the image one by one:
Problem 2171:
Write an expression for the area of the triangle. Simplify as much as possible.
a) Triangle with sides and
The area of a right-angled triangle is calculated as: Here, the base is and the height is . So the area is: This simplifies to:
b) Triangle with sides and
Similarly, the area of this triangle is: We expand this expression using distributive property: Thus, the area is:
Problem 2172:
Fill in the empty boxes so that the equations hold.
a)
To solve this, expand : We need , so .
The missing number is 1.
b)
Expand : We need , so .
The missing number is 10.
c)
Here, we compare the terms. We have: Expanding , we get:
So, the missing term is 3x.
Problem 2173:
Simplify as much as possible.
a)
Expand both terms: Now combine like terms: So the simplified expression is:
b)
Expand both terms: Now combine like terms: So the simplified expression is:
c)
Expand both terms: Now subtract the second expression from the first: So the simplified expression is:
d)
First, find a common denominator. The least common denominator is 12: Now combine them: The simplified expression is:
Do you have any specific question on any part? Would you like more details on any of these solutions?
Here are 5 related questions to explore:
- How would the area of a triangle change if the base or height is multiplied by a constant?
- What are some strategies to factor quadratic expressions quickly?
- How can you check if two expanded expressions are equivalent?
- How would you simplify more complex expressions like cubic polynomials?
- What are the benefits of finding common denominators when working with fractions?
Tip: When simplifying algebraic expressions, always look for like terms and common factors to reduce the complexity step by step.
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Math Problem Analysis
Mathematical Concepts
Geometry (Area of Triangle)
Algebra (Expansion and Simplification)
Equations and Expressions
Polynomial Operations
Formulas
Area of a Triangle: A = 1/2 * base * height
Distributive Property: a(b + c) = ab + ac
Combining Like Terms in Polynomials
Theorems
Distributive Property
Polynomial Addition and Subtraction
Suitable Grade Level
Grades 7-10
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