Question

A triangle's height is 4 feet longer than twice its base. If we use $b$ to represent the triangle's base, use a polynomial to represent the triangle's area in expanded form. A triangle's area can be calculated by $A=\frac{1}{2} b h,$ where $b$ stands for base, and $h$ stands for height. area $=$ ________ square feet

Name: Problem 36, Chapter 5: Open Resources for Community College Algebra
Uploaded: 2024-01-19T20:54:22-08:00
Duration: 1 min 32 s
Channel: Lynn Larson
Description: A triangle's height is 4 feet longer than twice its base. If we use b to represent the triangle's base, use a polynomial to represent the triangle's area in expanded form. A triangle's area can be calculated by A=(1)/(2) b h, where b stands for base, and h stands for height. area = square feet

   A triangle's height is 4 feet longer than twice its base. If we use $b$ to represent the triangle's base, use a polynomial to represent the triangle's area in expanded form. A triangle's area can be calculated by $A=\frac{1}{2} b h,$ where $b$ stands for base, and $h$ stands for height.
area $=$ ________ square feet

Open Resources for Community College Algebra

Portland Community… 1st Edition

Chapter 5, Problem 36

Instant Answer

Solved by Expert Lynn Larson

01/19/2024

Step 1

So, we can represent the height as $h = 2b + 4$. Now, we can use the formula for the area of a triangle: $A = \frac{1}{2}bh$. Substitute the expression for the height into the formula: $A = \frac{1}{2}b(2b + 4)$. Now, we can expand the expression: $A = Show more…

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A triangle's height is 4 feet longer than twice its base. If we use $b$ to represent the triangle's base, use a polynomial to represent the triangle's area in expanded form. A triangle's area can be calculated by $A=\frac{1}{2} b h,$ where $b$ stands for base, and $h$ stands for height. area $=$ ________ square feet

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Key Concepts

Triangle Area Formula

The triangle area formula, A = 1/2 * b * h, is a foundational concept in geometry that relates the base and height of a triangle to its area. This formula is essential for calculating how much space is enclosed by a triangle when its base and corresponding height are known.

Substitution into Algebraic Formulas

Substitution is a key algebraic technique where a variable in an equation is replaced with another expression that represents it. This allows us to express one quantity in terms of another, making it possible to solve problems that involve relationships between different variables.

Polynomial Expansion

Polynomial expansion involves applying distributive properties such as the distributive law to simplify products of algebraic expressions. This process transforms expressions into a standard form where similar terms are combined, enabling easier interpretation and further manipulation of the expression.

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