Finding Dimensions and Maximum Area for Geometric Shapes

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Discussion Overview

The discussion revolves around two mathematical problems related to geometric shapes: finding dimensions for a rectangular yard with a specified area and perimeter, and determining the maximum area of a right-angle triangle given its hypotenuse and perimeter. The scope includes mathematical reasoning and problem-solving techniques.

Discussion Character

  • Mathematical reasoning, Homework-related

Main Points Raised

  • One participant presents two questions regarding the dimensions of a yard enclosed by fencing and the maximum area of a triangle.
  • Another participant suggests that the first problem can be approached by setting up equations based on the perimeter and area of a rectangle.
  • A clarification is made that the yard is assumed to be rectangular in shape for the first problem.
  • For the second problem, a participant notes the relationships between the sides of the triangle and its perimeter, indicating that two equations can be formed with known and unknown variables.

Areas of Agreement / Disagreement

Participants generally agree on the approach to solving the problems by setting up equations, but the discussion does not resolve the specific solutions or methods to find the dimensions or maximum area.

Contextual Notes

Assumptions include the shape of the yard being rectangular and the relationships between the sides of the triangle being based on known geometric principles. The discussion does not delve into the details of solving the equations presented.

Who May Find This Useful

Students or individuals interested in geometric problem-solving, particularly those at a high school level or seeking to understand mathematical reasoning in geometry.

jess1515
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Hey I have two questions that I do not know how to answer...help? Please try to answer at a grade 10 level! And, this isn't a homework question.

1. A yard is to be enclosed by 40 meters of fencing. If all of the fencing is used, what dimensions will result in a yard with an area of 75m^2?

2. What is the maximum area of a right angle triangle whose hypotenuse is 10 cm and perimeter is 26 cm?
 
Last edited:
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#1:
You are saying that the perimeter is 40 meters. You should be able to develop this information:
\[<br /> \begin{array}{l}<br /> p = perimeter \\ <br /> 75 = theArea \\ <br /> p = 2x + 2y \\ <br /> 75 = xy \\ <br /> \end{array}<br /> \]<br />
 
Please note that in the above, I assumed that the yard is rectangular shaped.
 
Exactly, and if you use that method for #1, you end up with two equations and two variables which is easily solved.

For #2:
So you know that c^2=a^2+b^2
You also know that p=a+b+c
c and p are known variables, and b and a are your unknowns. Therefore, you once again have two equations and two unknowns: solvable.
 

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