An isosceles triangle, a triangle with two sides of equal...

Name: Problem 2, Chapter 4: Algebra A Combined Function
Uploaded: 2022-02-12T15:03:59-08:00
Duration: 2 min 45 s
Channel: Amanda Zielke
Description: An isosceles triangle, a triangle with two sides of equal length, has a perimeter of 20 inches. Each of the equal sides is one inch longer than the third side. Find the lengths of the three sides. a. 6 inches, 6 inches, and 7 inches b. 7 inches, 7 inches, and 6 inches c. 6 inches, 7 inches, and 8 inches

An isosceles triangle, a triangle with two sides of equal length, has a perimeter of 20 inches. Each of the equal sides is one inch longer than the third side. Find the lengths of the three sides. a. 6 inches, 6 inches, and 7 inches b. 7 inches, 7 inches, and 6 inches c. 6 inches, 7 inches, and 8 inches

An isosceles triangle, a triangle with two sides of equal length, has a perimeter of 20 inches. Each of the equal sides is one inch longer than the third side. Find the lengths of the three sides.
a. 6 inches, 6 inches, and 7 inches
b. 7 inches, 7 inches, and 6 inches
c. 6 inches, 7 inches, and 8 inches

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Key Concepts

Isosceles Triangle

An isosceles triangle is a type of triangle that has at least two sides of equal length. This property leads to several unique characteristics, such as congruent base angles, which often simplifies the process of solving geometric problems by reducing the number of unique variables involved.

Perimeter

The perimeter of any geometric shape, including a triangle, is the sum of the lengths of its sides. In problems involving triangles, knowing the perimeter enables the setup of an equation that connects the side lengths, which is crucial when additional relationships between the sides are provided.

Formulating Equations

Setting up equations based on given conditions is a fundamental algebraic method used to solve geometry problems. This involves translating a word problem into mathematical expressions, using the given relationships among the sides of the triangle, and then solving the resulting system of equations.

Solving Linear Equations

Once relationships are formulated into linear equations, solving them generally involves methods of algebra such as substitution or elimination. These techniques help determine unknown values and, in the context of geometric problems, reveal the dimensions of the sides, allowing one to fully understand the structure of the shape.

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