Mr. Brown has 46 metres of fence. He is thinking of fencing a piece of land around the back of his house for a garden
What shape garden could Mr. Brown create?
any shape he wants. Now, if you want it to be a polygon with integer sides, and one side of the garden is the back of the house, then it could be
a triangle with sides 23 and 23
a rectangle with sides 6, 20, 20 or many other sizes
a pentagon with sides 16, 10, 10, 10
and so on.
Rectangle, circle or triangle.
I doint have any
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To determine the shape of the garden Mr. Brown can create with 46 meters of fence, we need to consider different shapes and their corresponding perimeters to see if any match the given length.
Since Mr. Brown wants to create a garden around the back of his house, we can assume he wants to create a closed shape. Let's explore a few possible shapes he could consider:
1. Rectangle:
The perimeter of a rectangle is given by the formula P = 2(length + width). Since we don't have information about the width, we can only consider the possible lengths of the rectangle. Let's say the length of the rectangle is x meters. In that case, the perimeter of the rectangle would be P = 2(x + x) = 4x. Since we know P = 46 meters, we can set up the equation 4x = 46 and solve for x.
4x = 46
x = 46/4
x = 11.5 meters
If Mr. Brown chooses a rectangle shape, he could create a garden with dimensions 11.5 meters by any width within his property.
2. Square:
A square is a special case of a rectangle where all sides are equal. Therefore, if we assume the length and width of the square are both x meters, its perimeter would be P = 4x. Setting up the equation 4x = 46, we can solve for x.
4x = 46
x = 46/4
x = 11.5 meters
If Mr. Brown chooses a square shape, he could create a garden with dimensions 11.5 meters by 11.5 meters.
3. Circle:
Considering a circular garden, we need to calculate the circumference of the circle using the formula C = 2πr. Since we know the circumference C = 46 meters, we can set up the equation 2πr = 46 and solve for the radius.
2πr = 46
r = 46/(2π)
r ≈ 7.32 meters
If Mr. Brown chooses a circular shape, he could create a garden with a radius of approximately 7.32 meters.
Based on these options, Mr. Brown could create a rectangular garden with dimensions 11.5 meters by any width, a square garden with dimensions 11.5 meters by 11.5 meters, or a circular garden with a radius of approximately 7.32 meters.