The Lakeside Hotel is planning to build a shallow wading...

Name: Problem 96, Chapter 8: Intermediate Algebra for College Students
Uploaded: 2024-01-18T04:36:59-08:00
Duration: 2 min 12 s
Channel: Khushbu Rani
Description: The Lakeside Hotel is planning to build a shallow wading pool for children. If the pool is to be square and the diagonal of the square is 7 feet longer than a side, determine the length of one side of the pool.

The Lakeside Hotel is planning to build a shallow wading pool for children. If the pool is to be square and the diagonal of the square is 7 feet longer than a side, determine the length of one side of the pool.

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Key Concepts

Square Geometry

Square geometry involves understanding that a square is a regular quadrilateral with all sides equal and all angles equal to 90 degrees. This fundamental concept allows one to derive other properties, including relationships between the side lengths and the lengths of the diagonals.

Diagonal-Side Relationship

The diagonal of a square, by the Pythagorean theorem, is related to the side length through the formula: diagonal = side × ?2. This relationship is essential for translating geometric properties into algebraic terms, particularly when additional conditions are imposed on the lengths.

Algebraic Equation Solving

In problems that equate different expressions for a geometric quantity, algebraic equation solving is used to isolate the unknown variable. This process involves writing an equation based on the given geometric relationships and then applying algebraic techniques such as combining like terms, isolating the variable, and simplifying expressions.

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