# Finding Dimensions and Maximum Area for Geometric Shapes

• jess1515
In summary, the conversation is discussing two questions related to geometry. The first question involves finding the dimensions of a yard with a given perimeter and area, while the second question involves finding the maximum area of a right angle triangle with a given hypotenuse and perimeter. The speaker provides a method for solving each question by setting up and solving equations with two variables.
jess1515
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:
#1:
You are saying that the perimeter is 40 meters. You should be able to develop this information:
$$$\begin{array}{l} p = perimeter \\ 75 = theArea \\ p = 2x + 2y \\ 75 = xy \\ \end{array}$$$

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.

## What is the formula for finding the dimensions of an object using its area?

The formula for finding the dimensions of an object using its area is:

Length x Width = Area

## Can the formula be used for any shape?

Yes, the formula can be used for any shape as long as the area is known. However, the dimensions might be more complex for irregular shapes.

## What units should be used for the area and dimensions?

The units used for the area and dimensions should be consistent. For example, if the area is measured in square meters, the dimensions should also be in meters.

## Can the formula be used to find the dimensions of a 3-dimensional object?

No, the formula for finding dimensions using area only applies to 2-dimensional objects. To find the dimensions of a 3-dimensional object, you would need to use the formula for volume.

## Are there any other methods for finding dimensions besides using area?

Yes, there are other methods for finding dimensions such as using perimeter or volume. The method used will depend on the information available about the object.

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