Please answer #3 and #4. Due today! Will mark brainliest for best answer! :)
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The amount Cindy should increase in each dimension of the scaled model is 12 m.
<h3>What is a rectangular prism?</h3>It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape. It is also called a cuboid.
We have:
The scaled model of the container has dimensions 2m by 4m by 6m.
Volume of the scaled model = 2×4×6 = 48 cubic m
Let x be the amount by which each dimension is increased.
(2 + x)(4 + x)(6 + x) = 84(48)
The quadratic equation has no real solution so,
x = 12 m
Thus, the amount Cindy should increase in each dimension of the scaled model is 12 m.
Learn more about the rectangular prism here:
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The dimensions of the rectangle can be a length of 2ft and a width of 4ft.
<h3>How to find the dimensions of the garden?</h3>
Remember that for a rectangle of length L and width W, the perimeter is:
P = 2*(L + W)
And the area is:
A = L*W
In this case, we know that the area is 8 square feet and the perimeter is 12 ft, then we have a system of equations:
12ft = 2*(L + W)
8ft² = L*W
To solve this, we first need to isolate one of the variables in one of the equations, I will isolate L on the first one:
12ft/2 = L + W
6ft - W = L
Now we can replace that in the other equation to get:
8ft² = (6ft - W)*W
This is a quadratic equation:
-W^2 + 6ft*W - 8ft² = 0
The solutions are given by Bhaskara's formula:
Then we have two solutions:
W = (-6 - 2)/-2 = 4ft
W = (-6 + 2)/-2 = 2ft
If we take any of these solutions, the length will be equal to the other solution.
So the dimensions of the rectangle can be a length of 2ft and a width of 4ft.
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