What is the perimeter of a rectangle with a 3:2 ratio and an area of 294 dm2?

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Homework Help Overview

The problem involves a rectangle characterized by a 3:2 ratio of its sides and an area of 294 dm². Participants are seeking to determine the perimeter based on these parameters.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are discussing how to relate the given area and ratio to find the perimeter. Some are questioning the basic definitions of a rectangle and the formulas for area and perimeter. Others are attempting to express the dimensions in terms of a variable to facilitate calculations.

Discussion Status

There is an ongoing exploration of how to set up the problem using the given ratio and area. Some participants have suggested expressing the length and width in terms of a single variable, while others are still seeking clarification on the fundamental concepts involved.

Contextual Notes

Participants have noted the need to derive relationships from the ratio and area, but there is a lack of consensus on the next steps to take. Basic definitions and formulas are being revisited, indicating some uncertainty in foundational understanding.

EMEE_
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Homework Statement
A rectangle has a ratio of 3:2. The area is 294 dm2. What is the perimeter?
Relevant Equations
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Hi. Could someone please help me with this? :

A rectangle has a ratio of 3:2. The area is 294 dm2. What is the perimeter?
 
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How am I supposed to calculate this?
 
EMEE_ said:
How am I supposed to calculate this?
What is a rectangle? How do you calculate the area and the perimeter of a rectangle?
 
243519
So the area and ratio are given ( 3:2) and 3 represents the long side and 2 the shorter side. I calculate the area like this: A = L * W ( L is the length and W is the width). I think that the perimeter is 2*W+2*L
 
EMEE_ said:
View attachment 243519 So the area and ratio are given ( 3:2) and 3 represents the long side and 2 the shorter side. I calculate the area like this: A = L * W ( L is the length and W is the width). I think that the perimeter is 2*W+2*L
But you know that the ratio of the length to the width is 3/2, or ##\frac L W = \frac 3 2##. From this equation you can write the length in terms of the width.

Write your area equation using the value given, and write the equation for the perimeter. Keep in mind what I wrote above.
 
Let L=3x and W=2x, where x is unknown.
 

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