A supermarket, rectangular in shape and 200 feet by 300...

Name: Problem 1162, Chapter 38: Algebra and Trigonometry
Uploaded: 2021-05-15T08:19:34-08:00
Duration: 3 min 41 s
Channel: Wendi Zhao
Description: A supermarket, rectangular in shape and 200 feet by 300 feet, is to be built on a city block that contains 81,600 square feet. There will be a uniform strip around the building for parking. How wide is the strip?

A supermarket, rectangular in shape and 200 feet by 300 feet, is to be built on a city block that contains 81,600 square feet. There will be a uniform strip around the building for parking. How wide is the strip?

Key Concepts

Area Calculation

Understanding the area of a shape is fundamental to this problem. It involves computing the space inside a shape for both the building and the block. For a rectangle, the area is calculated by multiplying the length by the width. This concept is used to determine areas for both the supermarket and the city block to set up the problem properly.

Uniform Surrounding Strip

The uniform strip concept refers to having a consistent width of additional space all around the primary shape. In this context, the strip increases each dimension of the building by twice its width. Recognizing this is crucial to properly modeling the enlarged dimensions of the entire structure including the parking area.

Algebraic Equation Setup

Setting up an algebraic equation is key to linking the known area of the city block with the dimensions of the larger rectangle that includes both the building and the parking strip. This involves expressing the new dimensions in terms of the unknown strip width and equating the resulting area to the block's area.

Quadratic Equations

The process of setting up the equation often results in a quadratic equation in the unknown strip width due to the squared term that arises from multiplying the linear expressions for the length and width. Solving this quadratic equation is essential and may require techniques like factoring, completing the square, or using the quadratic formula.

Transcript

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