Question

Translate to an equation and solve. An architect believes that the optimal design for a new building is a rectangular shape where the length is four times the width. Budget restrictions force the building perimeter to be 300 feet. What will be the dimensions of the building?

Name: Problem 5, Chapter 4: Prealgebra
Uploaded: 2020-05-13T21:58:11-08:00
Duration: 3 min 3 s
Channel: Farnood Ensan
Description: Translate to an equation and solve. An architect believes that the optimal design for a new building is a rectangular shape where the length is four times the width. Budget restrictions force the building perimeter to be 300 feet. What will be the dimensions of the building?

   Translate to an equation and solve.
An architect believes that the optimal design for a new building is a rectangular shape where the length is four times the width. Budget restrictions force the building perimeter to be 300 feet. What will be the dimensions of the building?

Prealgebra

Tom Carson 4th Edition

Chapter 4, Problem 5

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Solved by Expert Farnood Ensan

05/13/2020

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We can represent this as an equation: \[l = 4w\] Show more…

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Translate to an equation and solve. An architect believes that the optimal design for a new building is a rectangular shape where the length is four times the width. Budget restrictions force the building perimeter to be 300 feet. What will be the dimensions of the building?

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Key Concepts

Algebraic Modeling

This concept involves translating real-world scenarios into mathematical equations. It requires identifying variables, understanding relationships between quantities, and expressing these relationships symbolically so that mathematical methods can be applied to find solutions.

Perimeter of a Rectangle

Understanding the formula for the perimeter of a rectangle is crucial. The perimeter is calculated as the sum of twice the width plus twice the length. This geometric concept is fundamental when solving problems that involve dimensions of rectangular shapes under specific constraints.

Solving Linear Equations

This involves simplifying and rearranging algebraic equations to isolate the unknown variable. In the context of the problem, it is used after substituting given relationships into the perimeter formula to determine the specific dimensions that satisfy all conditions.

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