Question

NO LINKS!!! NEED URGENT HELP!!!

1. Describe the shape of the graph and any special features you see.

2. What is the greatest area possible for a rectangle with this perimeter? What are the dimensions of this rectangle?

3. What is the area of the rectangle whose length is 10 meters? What is the area of the rectangle whose length is 30 meters> How are these rectangles related?

Answer 1

Answers:

1. The graph is in the shape of a parabola, there is a vertex point at (20, 400), and the zeros (x-intercepts) of the graph are at the origin of the coordinate plane (0, 0) and (40, 0).

2. The greatest area possible for a rectangle with a perimeter of 80 meters is 400
`m^2`, and the dimensions of this rectangle will be 20 meters in length and 20 meters in width.

3. The area of the rectangle whose length is 10 meters and the area of the rectangle whose length is 30 meters are the same, both being 300
`m^2`. This is because the perimeter is set as 80 meters total, and as they are both rectangles, the opposite sides must be the same length.

For the rectangle with a length of 10 meters, 2 of the 4 sides will use 20 meters of material, so there will be 60 meters of material left for the remaining 2 sides, or 30 meters per side. So the dimensions of that rectangle would be 10 meters in length and 30 meters in width.

For the rectangle with a length of 30 meters, it's the same thing, except the length is 30 meters, and the width is 10 meters. And for both rectangles, their areas are 30 meters multiplied by 10 meters, which equals 300
`m^(2)`, so the way these two rectangles are related is that they have the same area.

Have a great day! Feel free to let me know if you have any more questions :)

Answer 2

1. See below.

2. 400 m²

20 m x 20 m

3. 300 m²

Explanation:

Question 1

The graph is a parabola that opens downwards.

Its vertex is (20, 400) and its axis of symmetry is x = 20.

Question 2

From inspection of the given graph, the greatest possible area (y-value) is 400 m². This is when the length of the rectangle is 20 m.

The largest possible area of a rectangle is when the length equals the width. Therefore, the dimensions of the rectangle with the greatest area possible are:

• width = 20 m
• length = 20 m

Question 3

From inspection of the graph, when the length of the rectangle is 10 m, its area is 300 m².

Similarly, when the length of the rectangle is 30 m, its area is also 300 m².

A rectangle has two pairs of parallel sides of equal length.

Therefore, as both rectangles have the same area, this means that the one pair of parallel sides is 10 m in length and the other pair of parallel sides is 30 m in length. The dimensions of both rectangles are the same: 10 m x 30 m, where the width and length are interchangeable.