Question

Without actually solving each problem, choose each correct solution by deciding which choice satisfies the given conditions. 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

Name: Problem 2, Chapter 4: Beginning and Intermediate Algebra
Uploaded: 2020-03-12T06:02:27-08:00
Duration: 1 min 18 s
Channel: Surjit Tewari

   Without actually solving each problem, choose each correct solution by deciding which choice satisfies the given conditions.
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

Beginning and Intermediate Algebra

Elayn Martin-Gay 4th Edition

Chapter 4, Problem 2

Instant Answer

Solved by Expert Surjit Tewari

03/12/2020

Step 1

Let's denote these sides as 'a'. The third side is one inch shorter than the equal sides, so we denote it as 'b = a - 1'. Show more…

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Without actually solving each problem, choose each correct solution by deciding which choice satisfies the given conditions. 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 defined by having at least two sides of equal length, which also implies that the angles opposite those sides are equal. This property is fundamental in determining unknown side lengths or angles in problems involving triangles with symmetry.

Triangle Perimeter

The perimeter of a triangle is the total length around the triangle, obtained by summing the lengths of all three sides. Knowing the perimeter allows one to set up equations relating the side lengths when additional conditions are provided.

Algebraic Formulation of Geometric Relationships

Many geometry problems involve forming equations based on relationships between side lengths. By translating given conditions about a figure—such as one side being a fixed amount longer than another—into algebraic expressions, one can solve for unknown quantities without resorting to trial-and-error methods.

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