A rectangular garden in a backyard has an area of (3x^2+5x-6) square meters. It's width is (x+2) meters
A. Find the length of the garden
B. You decided to partition the garden into two or more smaller congruent gardens.Design a possible model and include mathematical concepts in your design
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draw a diagonal
A. To find the length of the garden, we can use the formula for the area of a rectangle: Area = Length x Width.
We are given that the area of the garden is (3x^2 + 5x - 6) square meters. And we know the width of the garden is (x + 2) meters. Let's replace the variables in the area expression with their respective values:
Area = Length x Width
(3x^2 + 5x - 6) = Length x (x + 2)
Now we can solve for the length by dividing both sides of the equation by (x + 2):
(3x^2 + 5x - 6) / (x + 2) = Length
This gives us the length of the garden.
B. To design a possible model of partitioning the garden into smaller congruent gardens, we need to consider that the total area of the garden should be divided equally into the smaller parts.
Let's say we want to partition the garden into four congruent smaller gardens.
1. First, find the total area of the garden by multiplying the length and width:
Total Area = Length x Width
Total Area = (3x^2 + 5x - 6) square meters
2. Divide the total area by the number of smaller gardens to get the area of each smaller garden. In this case, since we want four smaller gardens, divide the total area by 4:
Area of each smaller garden = Total Area / 4
3. Now we can find the length and width of each smaller garden. Divide the length of the garden by 2 to get the length of each smaller garden:
Length of each smaller garden = Length / 2
4. To ensure congruency, the width of each smaller garden should be the same as the width of the original garden:
Width of each smaller garden = Width
So, in the model, each smaller garden will have a length of (Length / 2) and a width of (Width).
By following these steps, you can design a possible model for partitioning the garden into two or more congruent smaller gardens.